id	sid	tid	token	lemma	pos
hjic-943	1	1	hungarian	hungarian	ADJ
hjic-943	1	2	journal	journal	NOUN
hjic-943	1	3	of	of	ADP
hjic-943	1	4	industrial	industrial	ADJ
hjic-943	1	5	chemistry	chemistry	NOUN
hjic-943	1	6	veszprem	veszprem	PROPN
hjic-943	1	7	vol	vol	NOUN
hjic-943	1	8	.	.	PROPN
hjic-943	2	1	30	30	NUM
hjic-943	2	2	.	.	PUNCT
hjic-943	3	1	pp	pp	ADJ
hjic-943	3	2	.	.	PUNCT
hjic-943	4	1	61	61	NUM
hjic-943	4	2	-71	-71	NUM
hjic-943	4	3	(	(	PUNCT
hjic-943	4	4	2002	2002	NUM
hjic-943	4	5	)	)	PUNCT
hjic-943	4	6	effect	effect	NOUN
hjic-943	4	7	of	of	ADP
hjic-943	4	8	steady	steady	ADJ
hjic-943	4	9	state	state	NOUN
hjic-943	4	10	assumption	assumption	NOUN
hjic-943	4	11	on	on	ADP
hjic-943	4	12	the	the	DET
hjic-943	4	13	structural	structural	ADJ
hjic-943	4	14	solvability	solvability	NOUN
hjic-943	4	15	of	of	ADP
hjic-943	4	16	dynamic	dynamic	ADJ
hjic-943	4	17	process	process	NOUN
hjic-943	4	18	models	model	NOUN
hjic-943	4	19	a.	a.	NOUN
hjic-943	4	20	leitold	leitold	PROPN
hjic-943	4	21	and	and	CCONJ
hjic-943	4	22	k.	k.	PROPN
hjic-943	4	23	m.	m.	PROPN
hjic-943	4	24	hangos1	hangos1	PROPN
hjic-943	4	25	•	•	ADV
hjic-943	4	26	2	2	NUM
hjic-943	4	27	(	(	PUNCT
hjic-943	4	28	department	department	NOUN
hjic-943	4	29	of	of	ADP
hjic-943	4	30	mathematics	mathematics	PROPN
hjic-943	4	31	,	,	PUNCT
hjic-943	4	32	university	university	NOUN
hjic-943	4	33	ofveszprem	ofveszprem	ADJ
hjic-943	4	34	,	,	PUNCT
hjic-943	4	35	p.o.b	p.o.b	NOUN
hjic-943	4	36	.	.	PUNCT
hjic-943	5	1	·	·	PUNCT
hjic-943	5	2	158	158	NUM
hjic-943	5	3	,	,	PUNCT
hjic-943	5	4	veszprem	veszprem	PROPN
hjic-943	5	5	,	,	PUNCT
hjic-943	5	6	h-8201	h-8201	PROPN
hjic-943	5	7	,	,	PUNCT
hjic-943	5	8	hungary	hungary	NOUN
hjic-943	5	9	1systems	1systems	NUM
hjic-943	5	10	and	and	CCONJ
hjic-943	5	11	control	control	PROPN
hjic-943	5	12	research	research	NOUN
hjic-943	5	13	laboratory	laboratory	NOUN
hjic-943	5	14	,	,	PUNCT
hjic-943	5	15	computer	computer	NOUN
hjic-943	5	16	and	and	CCONJ
hjic-943	5	17	automation	automation	NOUN
hjic-943	5	18	institute	institute	NOUN
hjic-943	5	19	has	have	AUX
hjic-943	5	20	,	,	PUNCT
hjic-943	5	21	p.o.b	p.o.b	VERB
hjic-943	5	22	.	.	PUNCT
hjic-943	6	1	63	63	NUM
hjic-943	6	2	,	,	PUNCT
hjic-943	6	3	budapest	budapest	NOUN
hjic-943	6	4	,	,	PUNCT
hjic-943	6	5	h-1518	h-1518	PROPN
hjic-943	6	6	,	,	PUNCT
hjic-943	6	7	hungary	hungary	NOUN
hjic-943	6	8	2department	2department	NUM
hjic-943	6	9	of	of	ADP
hjic-943	6	10	computer	computer	NOUN
hjic-943	6	11	science	science	NOUN
hjic-943	6	12	,	,	PUNCT
hjic-943	6	13	university	university	NOUN
hjic-943	6	14	ofveszprem	ofveszprem	ADJ
hjic-943	6	15	,	,	PUNCT
hjic-943	6	16	p.o.b	p.o.b	NOUN
hjic-943	6	17	.	.	PUNCT
hjic-943	7	1	158	158	NUM
hjic-943	7	2	,	,	PUNCT
hjic-943	7	3	veszprem	veszprem	PROPN
hjic-943	7	4	,	,	PUNCT
hjic-943	7	5	h-8201	h-8201	PROPN
hjic-943	7	6	,	,	PUNCT
hjic-943	7	7	hungary	hungary	PROPN
hjic-943	7	8	)	)	PUNCT
hjic-943	7	9	received	receive	VERB
hjic-943	7	10	:	:	PUNCT
hjic-943	7	11	july	july	PROPN
hjic-943	7	12	18	18	NUM
hjic-943	7	13	,	,	PUNCT
hjic-943	7	14	2001	2001	NUM
hjic-943	7	15	;	;	PUNCT
hjic-943	7	16	revised	revise	VERB
hjic-943	7	17	:	:	PUNCT
hjic-943	7	18	september	september	PROPN
hjic-943	7	19	24	24	NUM
hjic-943	7	20	,	,	PUNCT
hjic-943	7	21	2001	2001	NUM
hjic-943	7	22	the	the	DET
hjic-943	7	23	variable	variable	ADJ
hjic-943	7	24	structure	structure	NOUN
hjic-943	7	25	of	of	ADP
hjic-943	7	26	dynamic	dynamic	ADJ
hjic-943	7	27	process	process	NOUN
hjic-943	7	28	models	model	NOUN
hjic-943	7	29	is	be	AUX
hjic-943	7	30	represented	represent	VERB
hjic-943	7	31	by	by	ADP
hjic-943	7	32	a	a	DET
hjic-943	7	33	directed	direct	VERB
hjic-943	7	34	graph	graph	NOUN
hjic-943	7	35	termed	term	VERB
hjic-943	7	36	the	the	DET
hjic-943	7	37	representation	representation	NOUN
hjic-943	7	38	graph	graph	NOUN
hjic-943	7	39	for	for	ADP
hjic-943	7	40	the	the	DET
hjic-943	7	41	purpose	purpose	NOUN
hjic-943	7	42	of	of	ADP
hjic-943	7	43	solvability	solvability	NOUN
hjic-943	7	44	analysis	analysis	NOUN
hjic-943	7	45	in	in	ADP
hjic-943	7	46	this	this	DET
hjic-943	7	47	paper	paper	NOUN
hjic-943	7	48	.	.	PUNCT
hjic-943	8	1	structural	structural	ADJ
hjic-943	8	2	solvability	solvability	NOUN
hjic-943	8	3	analysis	analysis	NOUN
hjic-943	8	4	,	,	PUNCT
hjic-943	8	5	the	the	DET
hjic-943	8	6	determination	determination	NOUN
hjic-943	8	7	of	of	ADP
hjic-943	8	8	the	the	DET
hjic-943	8	9	structural	structural	ADJ
hjic-943	8	10	differential	differential	ADJ
hjic-943	8	11	index	index	NOUN
hjic-943	8	12	and	and	CCONJ
hjic-943	8	13	the	the	DET
hjic-943	8	14	structural	structural	ADJ
hjic-943	8	15	decomposition	decomposition	NOUN
hjic-943	8	16	of	of	ADP
hjic-943	8	17	the	the	DET
hjic-943	8	18	dae	dae	NOUN
hjic-943	8	19	model	model	NOUN
hjic-943	8	20	set	set	NOUN
hjic-943	8	21	can	can	AUX
hjic-943	8	22	be	be	AUX
hjic-943	8	23	performed	perform	VERB
hjic-943	8	24	using	use	VERB
hjic-943	8	25	the	the	DET
hjic-943	8	26	representation	representation	NOUN
hjic-943	8	27	graph	graph	NOUN
hjic-943	8	28	.	.	PUNCT
hjic-943	9	1	it	it	PRON
hjic-943	9	2	is	be	AUX
hjic-943	9	3	shown	show	VERB
hjic-943	9	4	that	that	SCONJ
hjic-943	9	5	the	the	DET
hjic-943	9	6	effect	effect	NOUN
hjic-943	9	7	of	of	ADP
hjic-943	9	8	steady	steady	ADJ
hjic-943	9	9	state	state	NOUN
hjic-943	9	10	assumption	assumption	NOUN
hjic-943	9	11	for	for	ADP
hjic-943	9	12	a	a	DET
hjic-943	9	13	state	state	NOUN
hjic-943	9	14	variable	variable	NOUN
hjic-943	9	15	:x	:x	PROPN
hjic-943	9	16	can	can	AUX
hjic-943	9	17	be	be	AUX
hjic-943	9	18	handled	handle	VERB
hjic-943	9	19	on	on	ADP
hjic-943	9	20	the	the	DET
hjic-943	9	21	representation	representation	NOUN
hjic-943	9	22	graph	graph	NOUN
hjic-943	9	23	by	by	ADP
hjic-943	9	24	modifying	modify	VERB
hjic-943	9	25	the	the	DET
hjic-943	9	26	assignment	assignment	NOUN
hjic-943	9	27	of	of	ADP
hjic-943	9	28	the	the	DET
hjic-943	9	29	derivative	derivative	ADJ
hjic-943	9	30	variable	variable	ADJ
hjic-943	9	31	vertex	vertex	NOUN
hjic-943	9	32	x	x	NOUN
hjic-943	9	33	'	'	NOUN
hjic-943	9	34	.	.	PUNCT
hjic-943	10	1	the	the	DET
hjic-943	10	2	method	method	NOUN
hjic-943	10	3	enables	enable	VERB
hjic-943	10	4	us	we	PRON
hjic-943	10	5	to	to	PART
hjic-943	10	6	select	select	VERB
hjic-943	10	7	a	a	DET
hjic-943	10	8	suitablr	suitablr	PROPN
hjic-943	10	9	modification	modification	NOUN
hjic-943	10	10	of	of	ADP
hjic-943	10	11	the	the	DET
hjic-943	10	12	original	original	ADJ
hjic-943	10	13	specification	specification	NOUN
hjic-943	10	14	such	such	ADJ
hjic-943	10	15	that	that	SCONJ
hjic-943	10	16	the	the	DET
hjic-943	10	17	structural	structural	ADJ
hjic-943	10	18	solvability	solvability	NOUN
hjic-943	10	19	and	and	CCONJ
hjic-943	10	20	the	the	DET
hjic-943	10	21	differential	differential	ADJ
hjic-943	10	22	index	index	NOUN
hjic-943	10	23	of	of	ADP
hjic-943	10	24	index	index	NOUN
hjic-943	10	25	1	1	NUM
hjic-943	10	26	process	process	NOUN
hjic-943	10	27	models	model	NOUN
hjic-943	10	28	remains	remain	VERB
hjic-943	10	29	unchanged	unchanged	ADJ
hjic-943	10	30	.	.	PUNCT
hjic-943	11	1	in	in	ADP
hjic-943	11	2	the	the	DET
hjic-943	11	3	case	case	NOUN
hjic-943	11	4	of	of	ADP
hjic-943	11	5	index	index	NOUN
hjic-943	11	6	2	2	NUM
hjic-943	11	7	models	model	NOUN
hjic-943	11	8	,	,	PUNCT
hjic-943	11	9	a	a	DET
hjic-943	11	10	steady	steady	ADJ
hjic-943	11	11	state	state	NOUN
hjic-943	11	12	assumption	assumption	NOUN
hjic-943	11	13	may	may	AUX
hjic-943	11	14	decrease	decrease	VERB
hjic-943	11	15	the	the	DET
hjic-943	11	16	differential	differential	ADJ
hjic-943	11	17	index	index	NOUN
hjic-943	11	18	of	of	ADP
hjic-943	11	19	the	the	DET
hjic-943	11	20	modified	modify	VERB
hjic-943	11	21	model	model	NOUN
hjic-943	11	22	to	to	ADP
hjic-943	11	23	i	i	PRON
hjic-943	11	24	if	if	SCONJ
hjic-943	11	25	the	the	DET
hjic-943	11	26	derivative	derivative	ADJ
hjic-943	11	27	variable	variable	NOUN
hjic-943	11	28	is	be	AUX
hjic-943	11	29	on	on	ADP
hjic-943	11	30	the	the	DET
hjic-943	11	31	underspecified	underspecified	ADJ
hjic-943	11	32	subgraph	subgraph	NOUN
hjic-943	11	33	.	.	PUNCT
hjic-943	12	1	the	the	DET
hjic-943	12	2	notions	notion	NOUN
hjic-943	12	3	and	and	CCONJ
hjic-943	12	4	methods	method	NOUN
hjic-943	12	5	are	be	AUX
hjic-943	12	6	illustrated	illustrate	VERB
hjic-943	12	7	on	on	ADP
hjic-943	12	8	simple	simple	ADJ
hjic-943	12	9	process	process	NOUN
hjic-943	12	10	examples	example	NOUN
hjic-943	12	11	.	.	PUNCT
hjic-943	13	1	keywords	keyword	NOUN
hjic-943	13	2	:	:	PUNCT
hjic-943	13	3	process	process	NOUN
hjic-943	13	4	models	model	NOUN
hjic-943	13	5	,	,	PUNCT
hjic-943	13	6	dae	dae	NOUN
hjic-943	13	7	models	model	NOUN
hjic-943	13	8	,	,	PUNCT
hjic-943	13	9	differential	differential	ADJ
hjic-943	13	10	index	index	NOUN
hjic-943	13	11	,	,	PUNCT
hjic-943	13	12	solvability	solvability	NOUN
hjic-943	13	13	,	,	PUNCT
hjic-943	13	14	structural	structural	ADJ
hjic-943	13	15	analysis	analysis	NOUN
hjic-943	13	16	,	,	PUNCT
hjic-943	13	17	steady	steady	ADJ
hjic-943	13	18	state	state	NOUN
hjic-943	13	19	assumption	assumption	NOUN
hjic-943	13	20	introduction	introduction	NOUN
hjic-943	13	21	lumped	lump	VERB
hjic-943	13	22	process	process	NOUN
hjic-943	13	23	models	model	NOUN
hjic-943	13	24	are	be	AUX
hjic-943	13	25	in	in	ADP
hjic-943	13	26	the	the	DET
hjic-943	13	27	form	form	NOUN
hjic-943	13	28	of	of	ADP
hjic-943	13	29	differential­	differential­	PRON
hjic-943	13	30	algebraic	algebraic	ADJ
hjic-943	13	31	equations	equation	NOUN
hjic-943	13	32	which	which	PRON
hjic-943	13	33	are	be	AUX
hjic-943	13	34	sometimes	sometimes	ADV
hjic-943	13	35	difficult	difficult	ADJ
hjic-943	13	36	to	to	PART
hjic-943	13	37	solve	solve	VERB
hjic-943	13	38	numerically	numerically	ADV
hjic-943	13	39	due	due	ADJ
hjic-943	13	40	to	to	ADP
hjic-943	13	41	index	index	NOUN
hjic-943	13	42	and	and	CCONJ
hjic-943	13	43	stiffness	stiffness	ADJ
hjic-943	13	44	problems	problem	NOUN
hjic-943	13	45	.	.	PUNCT
hjic-943	14	1	therefore	therefore	ADV
hjic-943	14	2	the	the	DET
hjic-943	14	3	solvability	solvability	NOUN
hjic-943	14	4	analysis	analysis	NOUN
hjic-943	14	5	of	of	ADP
hjic-943	14	6	differential­	differential­	PRON
hjic-943	14	7	algebraic	algebraic	ADJ
hjic-943	14	8	equations	equation	NOUN
hjic-943	14	9	(	(	PUNCT
hjic-943	14	10	dab	dab	PROPN
hjic-943	14	11	)	)	PUNCT
hjic-943	14	12	process	process	NOUN
hjic-943	14	13	models	model	NOUN
hjic-943	14	14	are	be	AUX
hjic-943	14	15	of	of	ADP
hjic-943	14	16	primary	primary	ADJ
hjic-943	14	17	importance	importance	NOUN
hjic-943	14	18	for	for	ADP
hjic-943	14	19	dynamic	dynamic	ADJ
hjic-943	14	20	simulation	simulation	NOUN
hjic-943	14	21	.	.	PUNCT
hjic-943	15	1	it	it	PRON
hjic-943	15	2	is	be	AUX
hjic-943	15	3	an	an	DET
hjic-943	15	4	important	important	ADJ
hjic-943	15	5	related	related	ADJ
hjic-943	15	6	question	question	NOUN
hjic-943	15	7	how	how	SCONJ
hjic-943	15	8	high	high	ADJ
hjic-943	15	9	index	index	NOUN
hjic-943	15	10	process	process	NOUN
hjic-943	15	11	models	model	NOUN
hjic-943	15	12	arise	arise	VERB
hjic-943	15	13	.	.	PUNCT
hjic-943	16	1	the	the	DET
hjic-943	16	2	effect	effect	NOUN
hjic-943	16	3	of	of	ADP
hjic-943	16	4	some	some	DET
hjic-943	16	5	decisions	decision	NOUN
hjic-943	16	6	taken	take	VERB
hjic-943	16	7	during	during	ADP
hjic-943	16	8	the	the	DET
hjic-943	16	9	modelling	modelling	NOUN
hjic-943	16	10	process	process	NOUN
hjic-943	16	11	on	on	ADP
hjic-943	16	12	the	the	DET
hjic-943	16	13	structural	structural	ADJ
hjic-943	16	14	solvability	solvability	NOUN
hjic-943	16	15	has	have	AUX
hjic-943	16	16	already	already	ADV
hjic-943	16	17	been	be	AUX
hjic-943	16	18	investigated	investigate	VERB
hjic-943	16	19	in	in	ADP
hjic-943	16	20	detail	detail	NOUN
hjic-943	16	21	[	[	X
hjic-943	16	22	8	8	NUM
hjic-943	16	23	]	]	PUNCT
hjic-943	16	24	.	.	PUNCT
hjic-943	17	1	it	it	PRON
hjic-943	17	2	is	be	AUX
hjic-943	17	3	known	know	VERB
hjic-943	17	4	that	that	SCONJ
hjic-943	17	5	the	the	DET
hjic-943	17	6	change	change	NOUN
hjic-943	17	7	in	in	ADP
hjic-943	17	8	the	the	DET
hjic-943	17	9	specification	specification	NOUN
hjic-943	17	10	may	may	AUX
hjic-943	17	11	transform	transform	VERB
hjic-943	17	12	an	an	DET
hjic-943	17	13	index	index	NOUN
hjic-943	17	14	1	1	NUM
hjic-943	17	15	model	model	NOUN
hjic-943	17	16	to	to	ADP
hjic-943	17	17	a	a	DET
hjic-943	17	18	higher	high	ADJ
hjic-943	17	19	index	index	NOUN
hjic-943	17	20	one	one	NUM
hjic-943	17	21	[	[	X
hjic-943	17	22	4j	4j	NOUN
hjic-943	17	23	.	.	PUNCT
hjic-943	18	1	it	it	PRON
hjic-943	18	2	is	be	AUX
hjic-943	18	3	also	also	ADV
hjic-943	18	4	known	know	VERB
hjic-943	18	5	that	that	SCONJ
hjic-943	18	6	algebraic	algebraic	ADJ
hjic-943	18	7	transformations	transformation	NOUN
hjic-943	18	8	,	,	PUNCT
hjic-943	18	9	that	that	PRON
hjic-943	18	10	is	be	AUX
hjic-943	18	11	transformations	transformation	NOUN
hjic-943	18	12	which	which	PRON
hjic-943	18	13	only	only	ADV
hjic-943	18	14	change	change	VERB
hjic-943	18	15	the	the	DET
hjic-943	18	16	algebraic	algebraic	ADJ
hjic-943	18	17	form	form	NOUN
hjic-943	18	18	of	of	ADP
hjic-943	18	19	a	a	DET
hjic-943	18	20	dae	dae	NOUN
hjic-943	18	21	model	model	NOUN
hjic-943	18	22	may	may	AUX
hjic-943	18	23	change	change	VERB
hjic-943	18	24	its	its	PRON
hjic-943	18	25	structural	structural	ADJ
hjic-943	18	26	solvability	solvability	NOUN
hjic-943	18	27	properties	property	NOUN
hjic-943	18	28	,	,	PUNCT
hjic-943	18	29	namely	namely	ADV
hjic-943	18	30	its	its	PRON
hjic-943	18	31	decomposition	decomposition	NOUN
hjic-943	18	32	in	in	ADP
hjic-943	18	33	a	a	DET
hjic-943	18	34	rather	rather	ADV
hjic-943	18	35	drastic	drastic	ADJ
hjic-943	18	36	way	way	NOUN
hjic-943	19	1	[	[	X
hjic-943	19	2	6	6	NUM
hjic-943	19	3	]	]	PUNCT
hjic-943	19	4	,	,	PUNCT
hjic-943	19	5	but	but	CCONJ
hjic-943	19	6	they	they	PRON
hjic-943	19	7	do	do	AUX
hjic-943	19	8	not	not	PART
hjic-943	19	9	change	change	VERB
hjic-943	19	10	the	the	DET
hjic-943	19	11	differential	differential	ADJ
hjic-943	19	12	index	index	NOUN
hjic-943	19	13	of	of	ADP
hjic-943	19	14	the	the	DET
hjic-943	19	15	model	model	NOUN
hjic-943	19	16	.	.	PUNCT
hjic-943	20	1	various	various	ADJ
hjic-943	20	2	methods	method	NOUN
hjic-943	20	3	and	and	CCONJ
hjic-943	20	4	techniques	technique	NOUN
hjic-943	20	5	have	have	AUX
hjic-943	20	6	been	be	AUX
hjic-943	20	7	proposed	propose	VERB
hjic-943	20	8	for	for	ADP
hjic-943	20	9	structural	structural	ADJ
hjic-943	20	10	solvability	solvability	NOUN
hjic-943	20	11	analysis	analysis	NOUN
hjic-943	20	12	based	base	VERB
hjic-943	20	13	on	on	ADP
hjic-943	20	14	both	both	CCONJ
hjic-943	20	15	algebraic	algebraic	PROPN
hjic-943	20	16	(	(	PUNCT
hjic-943	20	17	see	see	VERB
hjic-943	21	1	e.g.	e.g.	ADV
hjic-943	21	2	[	[	X
hjic-943	21	3	11	11	NUM
hjic-943	21	4	]	]	PUNCT
hjic-943	21	5	,	,	PUNCT
hjic-943	21	6	[	[	X
hjic-943	21	7	2j	2j	NOUN
hjic-943	21	8	)	)	PUNCT
hjic-943	21	9	and	and	CCONJ
hjic-943	21	10	graphical	graphical	ADJ
hjic-943	21	11	combinatorial	combinatorial	NOUN
hjic-943	21	12	(	(	PUNCT
hjic-943	21	13	[	[	X
hjic-943	21	14	9	9	NUM
hjic-943	21	15	]	]	PUNCT
hjic-943	21	16	,	,	PUNCT
hjic-943	21	17	[	[	X
hjic-943	21	18	12	12	NUM
hjic-943	21	19	]	]	PUNCT
hjic-943	21	20	,	,	PUNCT
hjic-943	21	21	[	[	X
hjic-943	21	22	loj	loj	ADJ
hjic-943	21	23	)	)	PUNCT
hjic-943	21	24	techniques	technique	NOUN
hjic-943	21	25	.	.	PUNCT
hjic-943	22	1	marquardt	marquardt	PROPN
hjic-943	22	2	et	et	PROPN
hjic-943	22	3	al	al	PROPN
hjic-943	22	4	.	.	PROPN
hjic-943	22	5	defined	define	VERB
hjic-943	22	6	a	a	DET
hjic-943	22	7	structural	structural	ADJ
hjic-943	22	8	approach	approach	NOUN
hjic-943	22	9	to	to	ADP
hjic-943	22	10	the	the	DET
hjic-943	22	11	characterization	characterization	NOUN
hjic-943	22	12	of	of	ADP
hjic-943	22	13	daes	daes	PROPN
hjic-943	22	14	which	which	PRON
hjic-943	22	15	is	be	AUX
hjic-943	22	16	derived	derive	VERB
hjic-943	22	17	from	from	ADP
hjic-943	22	18	symbolical	symbolical	ADJ
hjic-943	22	19	algorithm	algorithm	NOUN
hjic-943	22	20	fllj	fllj	NOUN
hjic-943	22	21	.	.	PUNCT
hjic-943	23	1	in	in	ADP
hjic-943	23	2	addition	addition	NOUN
hjic-943	23	3	to	to	ADP
hjic-943	23	4	this	this	PRON
hjic-943	23	5	,	,	PUNCT
hjic-943	23	6	two	two	NUM
hjic-943	23	7	systematically	systematically	ADV
hjic-943	23	8	different	different	ADJ
hjic-943	23	9	structural	structural	ADJ
hjic-943	23	10	approaches	approach	NOUN
hjic-943	23	11	were	be	AUX
hjic-943	23	12	applied	apply	VERB
hjic-943	23	13	to	to	PART
hjic-943	23	14	support	support	VERB
hjic-943	23	15	the	the	DET
hjic-943	23	16	development	development	NOUN
hjic-943	23	17	of	of	ADP
hjic-943	23	18	low	low	ADJ
hjic-943	23	19	index	index	NOUN
hjic-943	23	20	models	model	NOUN
hjic-943	23	21	.	.	PUNCT
hjic-943	24	1	it	it	PRON
hjic-943	24	2	is	be	AUX
hjic-943	24	3	intuitively	intuitively	ADV
hjic-943	24	4	clear	clear	ADJ
hjic-943	24	5	,	,	PUNCT
hjic-943	24	6	that	that	SCONJ
hjic-943	24	7	modelling	modelling	NOUN
hjic-943	24	8	assumptions	assumption	NOUN
hjic-943	24	9	may	may	AUX
hjic-943	24	10	drastically	drastically	ADV
hjic-943	24	11	affect	affect	VERB
hjic-943	24	12	the	the	DET
hjic-943	24	13	structur	structur	NOUN
hjic-943	24	14	:	:	PUNCT
hjic-943	24	15	u.	u.	NOUN
hjic-943	24	16	solv	solv	ADJ
hjic-943	24	17	~	~	NOUN
hjic-943	24	18	bility	bility	NOUN
hjic-943	24	19	properties	property	NOUN
hjic-943	24	20	of	of	ADP
hjic-943	24	21	a	a	DET
hjic-943	24	22	process	process	NOUN
hjic-943	24	23	model	model	NOUN
hjic-943	24	24	.	.	PUNCT
hjic-943	25	1	therefore	therefore	ADV
hjic-943	25	2	1	1	NUM
hjic-943	25	3	t	t	NOUN
hjic-943	25	4	is	be	AUX
hjic-943	25	5	of	of	ADP
hjic-943	25	6	pnmary	pnmary	ADJ
hjic-943	25	7	importance	importance	NOUN
hjic-943	25	8	to	to	PART
hjic-943	25	9	analyze	analyze	VERB
hjic-943	25	10	the	the	DET
hjic-943	25	11	effect	effect	NOUN
hjic-943	25	12	of	of	ADP
hjic-943	25	13	widely	widely	ADV
hjic-943	25	14	used	use	VERB
hjic-943	25	15	model	model	NOUN
hjic-943	25	16	specification	specification	NOUN
hjic-943	25	17	assumptions	assumption	NOUN
hjic-943	25	18	,	,	PUNCT
hjic-943	25	19	for	for	ADP
hjic-943	25	20	example	example	NOUN
hjic-943	25	21	the	the	DET
hjic-943	25	22	steady	steady	ADJ
hjic-943	25	23	state	state	NOUN
hjic-943	25	24	assumption	assumption	NOUN
hjic-943	25	25	on	on	ADP
hjic-943	25	26	the	the	DET
hjic-943	25	27	differential	differential	ADJ
hjic-943	25	28	index	index	NOUN
hjic-943	25	29	.	.	PUNCT
hjic-943	26	1	in	in	ADP
hjic-943	26	2	order	order	NOUN
hjic-943	26	3	.	.	PUNCT
hjic-943	27	1	to	to	PART
hjic-943	27	2	elllighten	elllighten	VERB
hjic-943	27	3	the	the	DET
hjic-943	27	4	importance	importance	NOUN
hjic-943	27	5	and	and	CCONJ
hjic-943	27	6	significance	significance	NOUN
hjic-943	27	7	of	of	ADP
hjic-943	27	8	analyzmg	analyzmg	NOUN
hjic-943	27	9	the	the	DET
hjic-943	27	10	solvability	solvability	NOUN
hjic-943	27	11	properties	property	NOUN
hjic-943	27	12	of	of	ADP
hjic-943	27	13	process	process	NOUN
hjic-943	27	14	models	model	NOUN
hjic-943	27	15	and	and	CCONJ
hjic-943	27	16	the	the	DET
hjic-943	27	17	effect	effect	NOUN
hjic-943	27	18	of	of	ADP
hjic-943	27	19	modelling	model	VERB
hjic-943	27	20	thereon	thereon	NOUN
hjic-943	27	21	we	we	PRON
hjic-943	27	22	should	should	AUX
hjic-943	27	23	recajj	recajj	VERB
hjic-943	27	24	~at	~at	NOUN
hjic-943	27	25	modelling	modelling	NOUN
hjic-943	27	26	is	be	AUX
hjic-943	27	27	one	one	NUM
hjic-943	27	28	of	of	ADP
hjic-943	27	29	the	the	DET
hjic-943	27	30	key	key	ADJ
hjic-943	27	31	and	and	CCONJ
hjic-943	27	32	most	most	ADJ
hjic-943	27	33	labour	labour	NOUN
hjic-943	27	34	..	..	PUNCT
hjic-943	27	35	consumm.g	consumm.g	VERB
hjic-943	27	36	activity	activity	NOUN
hjic-943	27	37	in	in	ADP
hjic-943	27	38	process	process	NOUN
hjic-943	27	39	system	system	NOUN
hjic-943	27	40	engineering	engineering	NOUN
hjic-943	27	41	serving	serve	VERB
hjic-943	27	42	as	as	ADP
hjic-943	27	43	a	a	DET
hjic-943	27	44	b	b	NOUN
hjic-943	27	45	~	~	NOUN
hjic-943	27	46	sts	st	NOUN
hjic-943	27	47	for	for	ADP
hjic-943	27	48	process	process	NOUN
hjic-943	27	49	flowsheeting	flowsheeting	NOUN
hjic-943	27	50	,	,	PUNCT
hjic-943	27	51	process	process	NOUN
hjic-943	27	52	control	control	NOUN
hjic-943	27	53	,	,	PUNCT
hjic-943	27	54	fault	fault	VERB
hjic-943	27	55	detection	detection	NOUN
hjic-943	27	56	and	and	CCONJ
hjic-943	27	57	diagnosis	diagnosis	NOUN
hjic-943	27	58	.	.	PUNCT
hjic-943	28	1	modelling	modelling	NOUN
hjic-943	28	2	assumptions	assumption	NOUN
hjic-943	28	3	can	can	AUX
hjic-943	28	4	be	be	AUX
hjic-943	28	5	seen	see	VERB
hjic-943	28	6	.	.	PUNCT
hjic-943	29	1	as	as	SCONJ
hjic-943	29	2	artifacts	artifact	NOUN
hjic-943	29	3	of	of	ADP
hjic-943	29	4	process	process	NOUN
hjic-943	29	5	modelling	model	VERB
hjic-943	29	6	being	be	AUX
hjic-943	29	7	a	a	DET
hjic-943	29	8	seq	seq	NOUN
hjic-943	29	9	~	~	NOUN
hjic-943	29	10	enttal­	enttal­	PART
hjic-943	29	11	iterative	iterative	ADJ
hjic-943	29	12	procedure	procedure	NOUN
hjic-943	29	13	with	with	ADP
hjic-943	29	14	the	the	DET
hjic-943	29	15	assumptions	assumption	NOUN
hjic-943	29	16	codmg	codmg	VERB
hjic-943	29	17	the	the	DET
hjic-943	29	18	decisions	decision	NOUN
hjic-943	29	19	of	of	ADP
hjic-943	29	20	the	the	DET
hjic-943	29	21	modeller	modeller	NOUN
hjic-943	29	22	.	.	PUNCT
hjic-943	30	1	in	in	ADP
hjic-943	30	2	the	the	DET
hjic-943	30	3	case	case	NOUN
hjic-943	30	4	of	of	ADP
hjic-943	30	5	problems	problem	NOUN
hjic-943	30	6	with	with	ADP
hjic-943	30	7	solving	solve	VERB
hjic-943	30	8	the	the	DET
hjic-943	30	9	model	model	NOUN
hjic-943	30	10	one	one	NOUN
hjic-943	30	11	is	be	AUX
hjic-943	30	12	interested	interested	ADJ
hjic-943	30	13	in	in	ADP
hjic-943	30	14	finding	find	VERB
hjic-943	30	15	the	the	DET
hjic-943	30	16	decisions	decision	NOUN
hjic-943	30	17	leading	lead	VERB
hjic-943	30	18	to	to	ADP
hjic-943	30	19	it	it	PRON
hjic-943	30	20	.	.	PUNCT
hjic-943	31	1	62	62	NUM
hjic-943	31	2	static	static	ADJ
hjic-943	31	3	and	and	CCONJ
hjic-943	31	4	dynamic	dynamic	ADJ
hjic-943	31	5	flowsheeting	flowsheeting	NOUN
hjic-943	31	6	packages	package	NOUN
hjic-943	31	7	nowadays	nowadays	ADV
hjic-943	31	8	are	be	AUX
hjic-943	31	9	almost	almost	ADV
hjic-943	31	10	all	all	PRON
hjic-943	31	11	equipped	equip	VERB
hjic-943	31	12	with	with	ADP
hjic-943	31	13	hpost	hpost	ADJ
hjic-943	31	14	mortem	mortem	NOUN
hjic-943	31	15	"	"	PUNCT
hjic-943	31	16	solvability	solvability	NOUN
hjic-943	31	17	analysis	analysis	NOUN
hjic-943	31	18	tools	tool	NOUN
hjic-943	31	19	but	but	CCONJ
hjic-943	31	20	these	these	PRON
hjic-943	31	21	can	can	AUX
hjic-943	31	22	not	not	PART
hjic-943	31	23	give	give	VERB
hjic-943	31	24	advice	advice	NOUN
hjic-943	31	25	on	on	ADP
hjic-943	31	26	how	how	SCONJ
hjic-943	31	27	to	to	PART
hjic-943	31	28	repair	repair	VERB
hjic-943	31	29	a	a	DET
hjic-943	31	30	model	model	NOUN
hjic-943	31	31	with	with	ADP
hjic-943	31	32	solvability	solvability	NOUN
hjic-943	31	33	problems	problem	NOUN
hjic-943	31	34	.	.	PUNCT
hjic-943	32	1	therefore	therefore	ADV
hjic-943	32	2	there	there	PRON
hjic-943	32	3	is	be	VERB
hjic-943	32	4	a	a	DET
hjic-943	32	5	growing	grow	VERB
hjic-943	32	6	demand	demand	NOUN
hjic-943	32	7	from	from	ADP
hjic-943	32	8	the	the	DET
hjic-943	32	9	users	user	NOUN
hjic-943	32	10	of	of	ADP
hjic-943	32	11	such	such	ADJ
hjic-943	32	12	packages	package	NOUN
hjic-943	32	13	to	to	PART
hjic-943	32	14	have	have	AUX
hjic-943	32	15	an	an	DET
hjic-943	32	16	intelligent	intelligent	ADJ
hjic-943	32	17	front	front	ADJ
hjic-943	32	18	-	-	PUNCT
hjic-943	32	19	end	end	NOUN
hjic-943	32	20	advisor	advisor	NOUN
hjic-943	32	21	to	to	PART
hjic-943	32	22	help	help	VERB
hjic-943	32	23	them	they	PRON
hjic-943	32	24	.	.	PUNCT
hjic-943	33	1	the	the	DET
hjic-943	33	2	current	current	ADJ
hjic-943	33	3	paper	paper	NOUN
hjic-943	33	4	can	can	AUX
hjic-943	33	5	be	be	AUX
hjic-943	33	6	regarded	regard	VERB
hjic-943	33	7	as	as	ADP
hjic-943	33	8	one	one	NUM
hjic-943	33	9	of	of	ADP
hjic-943	33	10	the	the	DET
hjic-943	33	11	first	first	ADJ
hjic-943	33	12	steps	step	NOUN
hjic-943	33	13	to	to	PART
hjic-943	33	14	achieve	achieve	VERB
hjic-943	33	15	this	this	DET
hjic-943	33	16	ambitious	ambitious	ADJ
hjic-943	33	17	goal	goal	NOUN
hjic-943	33	18	.	.	PUNCT
hjic-943	34	1	the	the	DET
hjic-943	34	2	graph	graph	NOUN
hjic-943	34	3	theoretical	theoretical	ADJ
hjic-943	34	4	method	method	NOUN
hjic-943	34	5	proposed	propose	VERB
hjic-943	34	6	by	by	ADP
hjic-943	34	7	murota	murota	NOUN
hjic-943	34	8	[	[	X
hjic-943	34	9	9	9	NUM
hjic-943	34	10	]	]	PUNCT
hjic-943	34	11	serves	serve	VERB
hjic-943	34	12	as	as	ADP
hjic-943	34	13	a	a	DET
hjic-943	34	14	basis	basis	NOUN
hjic-943	34	15	of	of	ADP
hjic-943	34	16	the	the	DET
hjic-943	34	17	analysis	analysis	NOUN
hjic-943	34	18	,	,	PUNCT
hjic-943	34	19	which	which	PRON
hjic-943	34	20	can	can	AUX
hjic-943	34	21	effectively	effectively	ADV
hjic-943	34	22	be	be	AUX
hjic-943	34	23	used	use	VERB
hjic-943	34	24	for	for	ADP
hjic-943	34	25	large	large	ADJ
hjic-943	34	26	systems	system	NOUN
hjic-943	34	27	with	with	ADP
hjic-943	34	28	several	several	ADJ
hjic-943	34	29	hundred	hundred	NUM
hjic-943	34	30	variables	variable	NOUN
hjic-943	34	31	.	.	PUNCT
hjic-943	35	1	this	this	DET
hjic-943	35	2	solvability	solvability	NOUN
hjic-943	35	3	analysis	analysis	NOUN
hjic-943	35	4	of	of	ADP
hjic-943	35	5	the	the	DET
hjic-943	35	6	model	model	NOUN
hjic-943	35	7	equations	equation	NOUN
hjic-943	35	8	gives	give	VERB
hjic-943	35	9	information	information	NOUN
hjic-943	35	10	on	on	ADP
hjic-943	35	11	the	the	DET
hjic-943	35	12	computa	computa	NOUN
hjic-943	35	13	~	~	NOUN
hjic-943	35	14	ion	ion	NOUN
hjic-943	35	15	order	order	NOUN
hjic-943	35	16	and	and	CCONJ
hjic-943	35	17	on	on	ADP
hjic-943	35	18	the	the	DET
hjic-943	35	19	size	size	NOUN
hjic-943	35	20	of	of	ADP
hjic-943	35	21	nonlinear	nonlinear	ADJ
hjic-943	35	22	sub	sub	NOUN
hjic-943	35	23	-	-	NOUN
hjic-943	35	24	sets	set	NOUN
hjic-943	35	25	fo	fo	SCONJ
hjic-943	35	26	equat10ns	equat10n	NOUN
hjic-943	35	27	to	to	PART
hjic-943	35	28	be	be	AUX
hjic-943	35	29	solved	solve	VERB
hjic-943	35	30	iteratively	iteratively	ADV
hjic-943	35	31	.	.	PUNCT
hjic-943	36	1	decompositions	decomposition	NOUN
hjic-943	36	2	of	of	ADP
hjic-943	36	3	the	the	DET
hjic-943	36	4	original	original	ADJ
hjic-943	36	5	dae	dae	NOUN
hjic-943	36	6	model	model	NOUN
hjic-943	36	7	are	be	AUX
hjic-943	36	8	used	use	VERB
hjic-943	36	9	for	for	ADP
hjic-943	36	10	detailed	detailed	ADJ
hjic-943	36	11	solvability	solvability	NOUN
hjic-943	36	12	analysis	analysis	NOUN
hjic-943	36	13	.	.	PUNCT
hjic-943	37	1	in	in	ADP
hjic-943	37	2	our	our	PRON
hjic-943	37	3	earlier	early	ADJ
hjic-943	37	4	work	work	NOUN
hjic-943	37	5	[	[	PUNCT
hjic-943	37	6	6	6	NUM
hjic-943	37	7	]	]	PUNCT
hjic-943	37	8	we	we	PRON
hjic-943	37	9	used	use	VERB
hjic-943	37	10	these	these	DET
hjic-943	37	11	graph­	graph­	NOUN
hjic-943	37	12	theoretical	theoretical	ADJ
hjic-943	37	13	methods	method	NOUN
hjic-943	37	14	for	for	ADP
hjic-943	37	15	index	index	NOUN
hjic-943	37	16	analysis	analysis	NOUN
hjic-943	37	17	of	of	ADP
hjic-943	37	18	dae	dae	NOUN
hjic-943	37	19	process	process	NOUN
hjic-943	37	20	models	model	NOUN
hjic-943	37	21	and	and	CCONJ
hjic-943	37	22	we	we	PRON
hjic-943	37	23	developed	develop	VERB
hjic-943	37	24	index	index	NOUN
hjic-943	37	25	reduction	reduction	NOUN
hjic-943	37	26	techniques	technique	NOUN
hjic-943	37	27	·	·	PUNCT
hjic-943	37	28	for	for	ADP
hjic-943	37	29	high	high	ADJ
hjic-943	37	30	index	index	NOUN
hjic-943	37	31	models	model	NOUN
hjic-943	37	32	based	base	VERB
hjic-943	37	33	thereon	thereon	NOUN
hjic-943	37	34	.	.	PUNCT
hjic-943	38	1	the	the	DET
hjic-943	38	2	graph	graph	NOUN
hjic-943	38	3	representation	representation	NOUN
hjic-943	38	4	of	of	ADP
hjic-943	38	5	dae	dae	NOUN
hjic-943	38	6	process	process	NOUN
hjic-943	38	7	models	model	NOUN
hjic-943	38	8	offers	offer	VERB
hjic-943	38	9	computationally	computationally	ADV
hjic-943	38	10	cheap	cheap	ADJ
hjic-943	38	11	methods	method	NOUN
hjic-943	38	12	for	for	ADP
hjic-943	38	13	analysing	analyse	VERB
hjic-943	38	14	.	.	PUNCT
hjic-943	39	1	t	t	PROPN
hjic-943	39	2	~	~	SYM
hjic-943	39	3	e	e	NOUN
hjic-943	39	4	differential	differential	ADJ
hjic-943	39	5	index	index	NOUN
hjic-943	39	6	and	and	CCONJ
hjic-943	39	7	structural	structural	ADJ
hjic-943	39	8	solvability	solvability	NOUN
hjic-943	39	9	decompositions	decomposition	NOUN
hjic-943	39	10	which	which	PRON
hjic-943	39	11	can	can	AUX
hjic-943	39	12	effectively	effectively	ADV
hjic-943	39	13	be	be	AUX
hjic-943	39	14	used	use	VERB
hjic-943	39	15	for	for	ADP
hjic-943	39	16	large	large	ADJ
hjic-943	39	17	systems	system	NOUN
hjic-943	39	18	.	.	PUNCT
hjic-943	40	1	in	in	ADP
hjic-943	40	2	this	this	DET
hjic-943	40	3	paper	paper	NOUN
hjic-943	40	4	our	our	PRON
hjic-943	40	5	aim	aim	NOUN
hjic-943	40	6	is	be	AUX
hjic-943	40	7	to	to	PART
hjic-943	40	8	investigate	investigate	VERB
hjic-943	40	9	how	how	SCONJ
hjic-943	40	10	a	a	DET
hjic-943	40	11	steady	steady	ADJ
hjic-943	40	12	state	state	NOUN
hjic-943	40	13	assumption	assumption	NOUN
hjic-943	40	14	for	for	ADP
hjic-943	40	15	a	a	DET
hjic-943	40	16	state	state	NOUN
hjic-943	40	17	variable	variable	NOUN
hjic-943	40	18	can	can	AUX
hjic-943	40	19	be	be	AUX
hjic-943	40	20	handled	handle	VERB
hjic-943	40	21	on	on	ADP
hjic-943	40	22	the	the	DET
hjic-943	40	23	representation	representation	NOUN
hjic-943	40	24	graph	graph	NOUN
hjic-943	40	25	and	and	CCONJ
hjic-943	40	26	what	what	PRON
hjic-943	40	27	is	be	AUX
hjic-943	40	28	the	the	DET
hjic-943	40	29	effect	effect	NOUN
hjic-943	40	30	of	of	ADP
hjic-943	40	31	this	this	DET
hjic-943	40	32	assumption	assumption	NOUN
hjic-943	40	33	on	on	ADP
hjic-943	40	34	the	the	DET
hjic-943	40	35	solvability	solvability	NOUN
hjic-943	40	36	properties	property	NOUN
hjic-943	40	37	of	of	ADP
hjic-943	40	38	the	the	DET
hjic-943	40	39	model	model	NOUN
hjic-943	40	40	in	in	ADP
hjic-943	40	41	general	general	ADJ
hjic-943	40	42	and	and	CCONJ
hjic-943	40	43	on	on	ADP
hjic-943	40	44	the	the	DET
hjic-943	40	45	differential	differential	ADJ
hjic-943	40	46	index	index	NOUN
hjic-943	40	47	,	,	PUNCT
hjic-943	40	48	in	in	ADP
hjic-943	40	49	particular	particular	ADJ
hjic-943	40	50	.	.	PUNCT
hjic-943	40	51	.	.	PUNCT
hjic-943	41	1	the	the	DET
hjic-943	41	2	paper	paper	NOUN
hjic-943	41	3	is	be	AUX
hjic-943	41	4	organised	organise	VERB
hjic-943	41	5	as	as	SCONJ
hjic-943	41	6	follows	follow	VERB
hjic-943	41	7	.	.	PUNCT
hjic-943	42	1	we	we	PRON
hjic-943	42	2	start	start	VERB
hjic-943	42	3	w1th	w1th	PUNCT
hjic-943	42	4	basic	basic	ADJ
hjic-943	42	5	notion	notion	NOUN
hjic-943	42	6	on	on	ADP
hjic-943	42	7	structural	structural	ADJ
hjic-943	42	8	solvability	solvability	NOUN
hjic-943	42	9	analysis	analysis	NOUN
hjic-943	42	10	and	and	CCONJ
hjic-943	42	11	on	on	ADP
hjic-943	42	12	the	the	DET
hjic-943	42	13	graph	graph	NOUN
hjic-943	42	14	representation	representation	NOUN
hjic-943	42	15	of	of	ADP
hjic-943	42	16	dae	dae	NOUN
hjic-943	42	17	process	process	NOUN
hjic-943	42	18	models	model	NOUN
hjic-943	42	19	in	in	ADP
hjic-943	42	20	the	the	DET
hjic-943	42	21	next	next	ADJ
hjic-943	42	22	section	section	NOUN
hjic-943	42	23	.	.	PUNCT
hjic-943	43	1	thereafter	thereafter	ADV
hjic-943	43	2	the	the	DET
hjic-943	43	3	effect	effect	NOUN
hjic-943	43	4	of	of	ADP
hjic-943	43	5	steady	steady	ADJ
hjic-943	43	6	state	state	NOUN
hjic-943	43	7	assumption	assumption	NOUN
hjic-943	43	8	on	on	ADP
hjic-943	43	9	the	the	DET
hjic-943	43	10	differential	differential	ADJ
hjic-943	43	11	index	index	NOUN
hjic-943	43	12	is	be	AUX
hjic-943	43	13	discussed	discuss	VERB
hjic-943	43	14	both	both	PRON
hjic-943	43	15	for	for	ADP
hjic-943	43	16	index	index	NOUN
hjic-943	43	17	1	1	NUM
hjic-943	43	18	and	and	CCONJ
hjic-943	43	19	higher	high	ADJ
hjic-943	43	20	index	index	NOUN
hjic-943	43	21	models	model	NOUN
hjic-943	43	22	.	.	PUNCT
hjic-943	44	1	finally	finally	ADV
hjic-943	44	2	conclusions	conclusion	NOUN
hjic-943	44	3	are	be	AUX
hjic-943	44	4	drawn	draw	VERB
hjic-943	44	5	.	.	PUNCT
hjic-943	45	1	basic	basic	ADJ
hjic-943	45	2	notions	notion	NOUN
hjic-943	45	3	the	the	DET
hjic-943	45	4	basic	basic	ADJ
hjic-943	45	5	notions	notion	NOUN
hjic-943	45	6	on	on	ADP
hjic-943	45	7	structural	structural	ADJ
hjic-943	45	8	solvability	solvability	NOUN
hjic-943	45	9	are	be	AUX
hjic-943	45	10	described	describe	VERB
hjic-943	45	11	here	here	ADV
hjic-943	45	12	for	for	ADP
hjic-943	45	13	both	both	CCONJ
hjic-943	45	14	algebraic	algebraic	ADJ
hjic-943	45	15	and	and	CCONJ
hjic-943	45	16	dae	dae	NOUN
hjic-943	45	17	models	model	NOUN
hjic-943	45	18	.	.	PUNCT
hjic-943	46	1	related	relate	VERB
hjic-943	46	2	questions	question	NOUN
hjic-943	46	3	.	.	PUNCT
hjic-943	47	1	such	such	ADJ
hjic-943	47	2	as	as	ADP
hjic-943	47	3	the	the	DET
hjic-943	47	4	representation	representation	NOUN
hjic-943	47	5	of	of	ADP
hjic-943	47	6	dae	dae	NOUN
hjic-943	47	7	models	model	NOUN
hjic-943	47	8	and	and	CCONJ
hjic-943	47	9	the	the	DET
hjic-943	47	10	handling	handling	NOUN
hjic-943	47	11	of	of	ADP
hjic-943	47	12	model	model	NOUN
hjic-943	47	13	specifications	specification	NOUN
hjic-943	47	14	are	be	AUX
hjic-943	47	15	also	also	ADV
hjic-943	47	16	discussed	discuss	VERB
hjic-943	47	17	.	.	PUNCT
hjic-943	48	1	from	from	ADP
hjic-943	48	2	the	the	DET
hjic-943	48	3	viewpoint	viewpoint	NOUN
hjic-943	48	4	of	of	ADP
hjic-943	48	5	the	the	DET
hjic-943	48	6	solvability	solvability	NOUN
hjic-943	48	7	.	.	PUNCT
hjic-943	49	1	the	the	DET
hjic-943	49	2	most	most	ADV
hjic-943	49	3	important	important	ADJ
hjic-943	49	4	characteristic	characteristic	ADJ
hjic-943	49	5	feature	feature	NOUN
hjic-943	49	6	of	of	ADP
hjic-943	49	7	process	process	NOUN
hjic-943	49	8	models	model	NOUN
hjic-943	49	9	is	be	AUX
hjic-943	49	10	the	the	DET
hjic-943	49	11	differential	differential	ADJ
hjic-943	49	12	index	index	NOUN
hjic-943	49	13	which	which	PRON
hjic-943	49	14	determines	determine	VERB
hjic-943	49	15	the	the	DET
hjic-943	49	16	difficulty	difficulty	NOUN
hjic-943	49	17	of	of	ADP
hjic-943	49	18	their	their	PRON
hjic-943	49	19	solution	solution	NOUN
hjic-943	49	20	.	.	PUNCT
hjic-943	50	1	therefore	therefore	ADV
hjic-943	50	2	the	the	DET
hjic-943	50	3	basic	basic	ADJ
hjic-943	50	4	notions	notion	NOUN
hjic-943	50	5	on	on	ADP
hjic-943	50	6	differential	differential	ADJ
hjic-943	50	7	index	index	NOUN
hjic-943	50	8	.	.	PUNCT
hjic-943	51	1	of	of	ADP
hjic-943	51	2	dae	dae	NOUN
hjic-943	51	3	models	model	NOUN
hjic-943	51	4	are	be	AUX
hjic-943	51	5	also	also	ADV
hjic-943	51	6	discussed	discuss	VERB
hjic-943	51	7	in	in	ADP
hjic-943	51	8	this	this	DET
hjic-943	51	9	section	section	NOUN
hjic-943	51	10	.	.	PUNCT
hjic-943	52	1	the	the	DET
hjic-943	52	2	structural	structural	ADJ
hjic-943	52	3	solvability	solvability	NOUN
hjic-943	52	4	of	of	ADP
hjic-943	52	5	a	a	DET
hjic-943	52	6	dae	dae	NOUN
hjic-943	52	7	model	model	NOUN
hjic-943	52	8	can	can	AUX
hjic-943	52	9	be	be	AUX
hjic-943	52	10	investigated	investigate	VERB
hjic-943	52	11	on	on	ADP
hjic-943	52	12	the	the	DET
hjic-943	52	13	so	so	ADV
hjic-943	52	14	-	-	PUNCT
hjic-943	52	15	called	call	VERB
hjic-943	52	16	representation	representation	NOUN
hjic-943	52	17	graph	graph	NOUN
hjic-943	52	18	(	(	PUNCT
hjic-943	52	19	9	9	NUM
hjic-943	52	20	]	]	PUNCT
hjic-943	52	21	.	.	PUNCT
hjic-943	53	1	structural	structural	ADJ
hjic-943	53	2	sol\·ability	sol\·ability	PROPN
hjic-943	53	3	as	as	ADP
hjic-943	53	4	a	a	DET
hjic-943	53	5	first	first	ADJ
hjic-943	53	6	step~	step~	NOUN
hjic-943	53	7	we	we	PRON
hjic-943	53	8	consider	consider	VERB
hjic-943	53	9	a	a	DET
hjic-943	53	10	.system	.system	NOUN
hjic-943	53	11	of	of	ADP
hjic-943	53	12	linear	linear	NOUN
hjic-943	53	13	or	or	CCONJ
hjic-943	53	14	non­	non­	PROPN
hjic-943	53	15	lin	lin	PROPN
hjic-943	53	16	~	~	SYM
hjic-943	53	17	ar	ar	PROPN
hjic-943	53	18	algebraic	algebraic	ADJ
hjic-943	53	19	equations	equation	NOUN
hjic-943	53	20	in	in	ADP
hjic-943	53	21	its	its	PRON
hjic-943	53	22	so	so	ADV
hjic-943	53	23	-	-	PUNCT
hjic-943	53	24	called	call	VERB
hjic-943	53	25	standard	standard	ADJ
hjic-943	53	26	form	form	NOUN
hjic-943	53	27	[	[	X
hjic-943	53	28	9	9	NUM
hjic-943	53	29	):	):	PUNCT
hjic-943	53	30	y	y	NOUN
hjic-943	53	31	,	,	PUNCT
hjic-943	53	32	=	=	PUNCT
hjic-943	53	33	ft(:r.u	ft(:r.u	NOUN
hjic-943	53	34	)	)	PUNCT
hjic-943	53	35	.	.	PUNCT
hjic-943	54	1	i	i	PRON
hjic-943	54	2	=	=	NOUN
hjic-943	54	3	i.	i.	PROPN
hjic-943	54	4	....	....	PUNCT
hjic-943	55	1	m	m	VERB
hjic-943	55	2	(	(	PUNCT
hjic-943	55	3	i	i	NOUN
hjic-943	55	4	)	)	PUNCT
hjic-943	55	5	(	(	PUNCT
hjic-943	55	6	2	2	X
hjic-943	55	7	)	)	PUNCT
hjic-943	55	8	wherexj	wherexj	NOUN
hjic-943	55	9	,	,	PUNCT
hjic-943	55	10	(	(	PUNCT
hjic-943	55	11	j	j	NOUN
hjic-943	55	12	=	=	SYM
hjic-943	55	13	1	1	NUM
hjic-943	55	14	,	,	PUNCT
hjic-943	55	15	...	...	PUNCT
hjic-943	55	16	,	,	PUNCT
hjic-943	55	17	n	n	CCONJ
hjic-943	55	18	)	)	PUNCT
hjic-943	55	19	and	and	CCONJ
hjic-943	55	20	uh	uh	INTJ
hjic-943	55	21	(	(	PUNCT
hjic-943	55	22	k	k	NOUN
hjic-943	55	23	=	=	SYM
hjic-943	55	24	1	1	NUM
hjic-943	55	25	,	,	PUNCT
hjic-943	55	26	...	...	PUNCT
hjic-943	55	27	,	,	PUNCT
hjic-943	55	28	k	k	X
hjic-943	55	29	)	)	PUNCT
hjic-943	55	30	ar~	ar~	PROPN
hjic-943	55	31	unknown	unknown	NOUN
hjic-943	55	32	,	,	PUNCT
hjic-943	55	33	y	y	PROPN
hjic-943	55	34	·	·	PUNCT
hjic-943	55	35	(	(	PUNCT
hjic-943	55	36	i	i	NOUN
hjic-943	55	37	=	=	NOUN
hjic-943	55	38	1	1	NUM
hjic-943	55	39	,	,	PUNCT
hjic-943	55	40	...	...	PUNCT
hjic-943	55	41	,	,	PUNCT
hjic-943	55	42	m	m	VERB
hjic-943	55	43	)	)	PUNCT
hjic-943	55	44	are	be	AUX
hjic-943	55	45	known	know	VERB
hjic-943	55	46	parameters	parameter	NOUN
hjic-943	55	47	,	,	PUNCT
hjic-943	55	48	fi	fi	NOUN
hjic-943	55	49	,	,	PUNCT
hjic-943	55	50	(	(	PUNCT
hjic-943	55	51	z	z	NOUN
hjic-943	55	52	=	=	SYM
hjic-943	55	53	1	1	NUM
hjic-943	55	54	,	,	PUNCT
hjic-943	55	55	...	...	PUNCT
hjic-943	55	56	,	,	PUNCT
hjic-943	55	57	m	m	PROPN
hjic-943	55	58	)	)	PUNCT
hjic-943	55	59	a	a	PRON
hjic-943	55	60	~	~	PROPN
hjic-943	55	61	d	d	X
hjic-943	55	62	gh	gh	PROPN
hjic-943	55	63	(	(	PUNCT
hjic-943	55	64	k	k	NOUN
hjic-943	55	65	=	=	SYM
hjic-943	55	66	1	1	NUM
hjic-943	55	67	,	,	PUNCT
hjic-943	55	68	...	...	PUNCT
hjic-943	55	69	,	,	PUNCT
hjic-943	55	70	k	k	X
hjic-943	55	71	)	)	PUNCT
hjic-943	55	72	are	be	AUX
hjic-943	55	73	assumed	assume	VERB
hjic-943	55	74	to	to	PART
hjic-943	55	75	be	be	AUX
hjic-943	55	76	sufficiently	sufficiently	ADV
hjic-943	55	77	smooth	smooth	ADJ
hjic-943	55	78	real	real	ADV
hjic-943	55	79	-	-	PUNCT
hjic-943	55	80	valued	value	VERB
hjic-943	55	81	functions	function	NOUN
hjic-943	55	82	.	.	PUNCT
hjic-943	56	1	we	we	PRON
hjic-943	56	2	assume	assume	VERB
hjic-943	56	3	that	that	SCONJ
hjic-943	56	4	the	the	DET
hjic-943	56	5	partial	partial	ADJ
hjic-943	56	6	derivatives	derivative	NOUN
hjic-943	56	7	of	of	ADP
hjic-943	56	8	functic	functic	ADJ
hjic-943	56	9	:	:	PUNCT
hjic-943	56	10	ms	ms	PROPN
hjic-943	56	11	t	t	PROPN
hjic-943	56	12	and	and	CCONJ
hjic-943	56	13	gk	gk	PROPN
hjic-943	56	14	are	be	AUX
hjic-943	56	15	elements	element	NOUN
hjic-943	56	16	of	of	ADP
hjic-943	56	17	a	a	DET
hjic-943	56	18	field	field	NOUN
hjic-943	56	19	j	j	NOUN
hjic-943	56	20	that	that	PRON
hjic-943	56	21	is	be	AUX
hjic-943	56	22	an	an	DET
hjic-943	56	23	extension	extension	NOUN
hjic-943	56	24	of	of	ADP
hjic-943	56	25	the	the	DET
hjic-943	56	26	rational	rational	ADJ
hjic-943	56	27	number	number	NOUN
hjic-943	56	28	field	field	NOUN
hjic-943	56	29	.2	.2	NUM
hjic-943	56	30	.	.	PUNCT
hjic-943	57	1	the	the	DET
hjic-943	57	2	system	system	NOUN
hjic-943	57	3	of	of	ADP
hjic-943	57	4	equations	equation	NOUN
hjic-943	57	5	above	above	ADV
hjic-943	57	6	is	be	AUX
hjic-943	57	7	structurally	structurally	ADV
hjic-943	57	8	solvable	solvable	ADJ
hjic-943	57	9	,	,	PUNCT
hjic-943	57	10	if	if	SCONJ
hjic-943	57	11	the	the	DET
hjic-943	57	12	jacobian	jacobian	ADJ
hjic-943	57	13	matrix	matrix	NOUN
hjic-943	57	14	j(x	j(x	PROPN
hjic-943	57	15	,	,	PUNCT
hjic-943	57	16	u	u	NOUN
hjic-943	57	17	)	)	PUNCT
hjic-943	57	18	as	as	ADP
hjic-943	57	19	a	a	DET
hjic-943	57	20	matrix	matrix	NOUN
hjic-943	57	21	over	over	ADP
hjic-943	57	22	:	:	PUNCT
hjic-943	57	23	j	j	NOUN
hjic-943	57	24	,	,	PUNCT
hjic-943	57	25	is	be	AUX
hjic-943	57	26	non	non	ADJ
hjic-943	57	27	-	-	ADJ
hjic-943	57	28	singular	singular	ADJ
hjic-943	57	29	,	,	PUNCT
hjic-943	57	30	where	where	SCONJ
hjic-943	57	31	[	[	PUNCT
hjic-943	57	32	j(f	j(f	PROPN
hjic-943	57	33	,	,	PUNCT
hjic-943	57	34	x	x	NOUN
hjic-943	57	35	)	)	PUNCT
hjic-943	57	36	j(f	j(f	PROPN
hjic-943	57	37	,	,	PUNCT
hjic-943	57	38	u	u	NOUN
hjic-943	57	39	)	)	PUNCT
hjic-943	57	40	j	j	PROPN
hjic-943	57	41	j	j	PROPN
hjic-943	57	42	x	x	PROPN
hjic-943	57	43	,	,	PUNCT
hjic-943	57	44	u	u	NOUN
hjic-943	57	45	)	)	PUNCT
hjic-943	57	46	=	=	SYM
hjic-943	57	47	(	(	PUNCT
hjic-943	57	48	j(g	j(g	X
hjic-943	57	49	,	,	PUNCT
hjic-943	57	50	x	x	NOUN
hjic-943	57	51	)	)	PUNCT
hjic-943	57	52	j(g	j(g	NOUN
hjic-943	57	53	,	,	PUNCT
hjic-943	57	54	u)ik	u)ik	PROPN
hjic-943	57	55	(	(	PUNCT
hjic-943	57	56	3	3	NUM
hjic-943	57	57	)	)	PUNCT
hjic-943	57	58	[	[	PUNCT
hjic-943	57	59	at	at	ADP
hjic-943	57	60	,	,	PUNCT
hjic-943	57	61	.	.	PUNCT
hjic-943	58	1	j	j	PROPN
hjic-943	58	2	j(f	j(f	PROPN
hjic-943	58	3	,	,	PUNCT
hjic-943	58	4	x	x	NOUN
hjic-943	58	5	)	)	PUNCT
hjic-943	58	6	=	=	PUNCT
hjic-943	59	1	ax~	ax~	PROPN
hjic-943	59	2	'	'	PUNCT
hjic-943	59	3	j(f	j(f	PROPN
hjic-943	59	4	,	,	PUNCT
hjic-943	59	5	u	u	NOUN
hjic-943	59	6	)	)	PUNCT
hjic-943	59	7	=	=	SYM
hjic-943	59	8	-~	-~	PROPN
hjic-943	59	9	[	[	PUNCT
hjic-943	59	10	at	at	ADP
hjic-943	59	11	,	,	PUNCT
hjic-943	59	12	.	.	PUNCT
hjic-943	60	1	j	j	X
hjic-943	60	2	~	~	PUNCT
hjic-943	60	3	aul	aul	NOUN
hjic-943	60	4	(	(	PUNCT
hjic-943	60	5	4	4	NUM
hjic-943	60	6	)	)	PUNCT
hjic-943	60	7	[	[	PUNCT
hjic-943	60	8	agk	agk	PROPN
hjic-943	60	9	j	j	PROPN
hjic-943	60	10	j(g	j(g	PROPN
hjic-943	60	11	,	,	PUNCT
hjic-943	60	12	x	x	X
hjic-943	60	13	)	)	PUNCT
hjic-943	60	14	=	=	PUNCT
hjic-943	61	1	axj	axj	NOUN
hjic-943	61	2	,	,	PUNCT
hjic-943	61	3	[	[	X
hjic-943	61	4	agk	agk	X
hjic-943	61	5	]	]	X
hjic-943	61	6	j(g	j(g	NOUN
hjic-943	61	7	,	,	PUNCT
hjic-943	61	8	u)=	u)=	NOUN
hjic-943	61	9	aul	aul	NOUN
hjic-943	61	10	(	(	PUNCT
hjic-943	61	11	5	5	NUM
hjic-943	61	12	)	)	PUNCT
hjic-943	61	13	and	and	CCONJ
hjic-943	61	14	ik	ik	PROPN
hjic-943	61	15	is	be	AUX
hjic-943	61	16	the	the	DET
hjic-943	61	17	k	k	PROPN
hjic-943	61	18	x	x	SYM
hjic-943	61	19	k	k	NOUN
hjic-943	61	20	identity	identity	NOUN
hjic-943	61	21	matrix	matrix	NOUN
hjic-943	61	22	.	.	PUNCT
hjic-943	62	1	it	it	PRON
hjic-943	62	2	is	be	AUX
hjic-943	62	3	possible	possible	ADJ
hjic-943	62	4	to	to	PART
hjic-943	62	5	consider	consider	VERB
hjic-943	62	6	the	the	DET
hjic-943	62	7	standard	standard	ADJ
hjic-943	62	8	form	form	NOUN
hjic-943	62	9	with	with	ADP
hjic-943	62	10	no	no	DET
hjic-943	62	11	loss	loss	NOUN
hjic-943	62	12	of	of	ADP
hjic-943	62	13	generality	generality	NOUN
hjic-943	62	14	in	in	ADP
hjic-943	62	15	such	such	DET
hjic-943	62	16	a	a	DET
hjic-943	62	17	way	way	NOUN
hjic-943	62	18	that	that	PRON
hjic-943	62	19	the	the	DET
hjic-943	62	20	variables	variable	NOUN
hjic-943	62	21	in	in	ADP
hjic-943	62	22	left­	left­	PROPN
hjic-943	62	23	hand	hand	NOUN
hjic-943	62	24	side	side	NOUN
hjic-943	62	25	of	of	ADP
hjic-943	62	26	equations	equation	NOUN
hjic-943	62	27	appear	appear	VERB
hjic-943	62	28	only	only	ADV
hjic-943	62	29	once	once	ADV
hjic-943	62	30	[	[	X
hjic-943	62	31	9	9	NUM
hjic-943	62	32	]	]	PUNCT
hjic-943	62	33	.	.	PUNCT
hjic-943	63	1	consider	consider	VERB
hjic-943	63	2	a	a	DET
hjic-943	63	3	system	system	NOUN
hjic-943	63	4	of	of	ADP
hjic-943	63	5	equations	equation	NOUN
hjic-943	63	6	in	in	ADP
hjic-943	63	7	the	the	DET
hjic-943	63	8	standard	standard	ADJ
hjic-943	63	9	form	form	NOUN
hjic-943	63	10	.	.	PUNCT
hjic-943	64	1	we	we	PRON
hjic-943	64	2	construct	construct	VERB
hjic-943	64	3	a	a	DET
hjic-943	64	4	directed	direct	VERB
hjic-943	64	5	graph	graph	NOUN
hjic-943	64	6	to	to	PART
hjic-943	64	7	represent	represent	VERB
hjic-943	64	8	the	the	DET
hjic-943	64	9	structure	structure	NOUN
hjic-943	64	10	of	of	ADP
hjic-943	64	11	the	the	DET
hjic-943	64	12	set	set	NOUN
hjic-943	64	13	of	of	ADP
hjic-943	64	14	equations	equation	NOUN
hjic-943	64	15	in	in	ADP
hjic-943	64	16	the	the	DET
hjic-943	64	17	following	following	ADJ
hjic-943	64	18	way	way	NOUN
hjic-943	64	19	.	.	PUNCT
hjic-943	65	1	the	the	DET
hjic-943	65	2	vertex­	vertex­	NOUN
hjic-943	65	3	set	set	NOUN
hjic-943	65	4	corresponding	correspond	VERB
hjic-943	65	5	to	to	ADP
hjic-943	65	6	unknowns	unknown	NOUN
hjic-943	65	7	and	and	CCONJ
hjic-943	65	8	parameters	parameter	NOUN
hjic-943	65	9	is	be	AUX
hjic-943	65	10	partitioned	partition	VERB
hjic-943	65	11	as	as	ADP
hjic-943	65	12	xu	xu	PROPN
hjic-943	65	13	u	u	PROPN
hjic-943	65	14	u	u	PROPN
hjic-943	65	15	y	y	PROPN
hjic-943	65	16	,	,	PUNCT
hjic-943	65	17	where	where	SCONJ
hjic-943	65	18	x=	x=	PUNCT
hjic-943	65	19	{	{	PUNCT
hjic-943	65	20	xi	xi	PROPN
hjic-943	65	21	>	>	X
hjic-943	65	22	·	·	PUNCT
hjic-943	65	23	·	·	PUNCT
hjic-943	65	24	·	·	PUNCT
hjic-943	65	25	'	'	PUNCT
hjic-943	65	26	xn	xn	NUM
hjic-943	65	27	}	}	PUNCT
hjic-943	65	28	,	,	PUNCT
hjic-943	65	29	u	u	NOUN
hjic-943	65	30	=	=	PRON
hjic-943	65	31	=	=	X
hjic-943	65	32	{	{	PUNCT
hjic-943	65	33	ur	ur	INTJ
hjic-943	65	34	,	,	PUNCT
hjic-943	65	35	...	...	PUNCT
hjic-943	65	36	,	,	PUNCT
hjic-943	65	37	uk	uk	PROPN
hjic-943	65	38	}	}	PUNCT
hjic-943	65	39	and	and	CCONJ
hjic-943	65	40	y	y	PROPN
hjic-943	66	1	=	=	PRON
hjic-943	66	2	=	=	X
hjic-943	66	3	{	{	PUNCT
hjic-943	66	4	yt	yt	PROPN
hjic-943	66	5	.	.	PROPN
hjic-943	66	6	·	·	PUNCT
hjic-943	66	7	·	·	PUNCT
hjic-943	66	8	·	·	PUNCT
hjic-943	66	9	,	,	PUNCT
hjic-943	66	10	ym	ym	PROPN
hjic-943	66	11	}	}	PUNCT
hjic-943	66	12	.	.	PUNCT
hjic-943	67	1	the	the	DET
hjic-943	67	2	functional	functional	ADJ
hjic-943	67	3	dependence	dependence	NOUN
hjic-943	67	4	corresponding	correspond	VERB
hjic-943	67	5	to	to	ADP
hjic-943	67	6	the	the	DET
hjic-943	67	7	equations	equation	NOUN
hjic-943	67	8	is	be	AUX
hjic-943	67	9	expressed	express	VERB
hjic-943	67	10	by	by	ADP
hjic-943	67	11	arcs	arc	NOUN
hjic-943	67	12	coming	come	VERB
hjic-943	67	13	into	into	ADP
hjic-943	67	14	yi	yi	NOUN
hjic-943	67	15	or	or	CCONJ
hjic-943	67	16	uk	uk	PROPN
hjic-943	67	17	respectively	respectively	ADV
hjic-943	67	18	from	from	ADP
hjic-943	67	19	those	those	DET
hjic-943	67	20	xj	xj	NOUN
hjic-943	67	21	and	and	CCONJ
hjic-943	67	22	u1	u1	PROPN
hjic-943	67	23	,	,	PUNCT
hjic-943	67	24	which	which	PRON
hjic-943	67	25	appear	appear	VERB
hjic-943	67	26	on	on	ADP
hjic-943	67	27	the	the	DET
hjic-943	67	28	right	right	ADJ
hjic-943	67	29	-	-	PUNCT
hjic-943	67	30	hand	hand	NOUN
hjic-943	67	31	side	side	NOUN
hjic-943	67	32	.	.	PUNCT
hjic-943	68	1	this	this	DET
hjic-943	68	2	graph	graph	NOUN
hjic-943	68	3	is	be	AUX
hjic-943	68	4	called	call	VERB
hjic-943	68	5	the	the	DET
hjic-943	68	6	representation	representation	NOUN
hjic-943	68	7	graph	graph	NOUN
hjic-943	68	8	of	of	ADP
hjic-943	68	9	the	the	DET
hjic-943	68	10	system	system	NOUN
hjic-943	68	11	of	of	ADP
hjic-943	68	12	equations	equation	NOUN
hjic-943	68	13	.	.	PUNCT
hjic-943	69	1	it	it	PRON
hjic-943	69	2	is	be	AUX
hjic-943	69	3	denoted	denote	VERB
hjic-943	69	4	by	by	ADP
hjic-943	69	5	g	g	PROPN
hjic-943	69	6	=	=	SYM
hjic-943	69	7	=	=	SYM
hjic-943	69	8	(	(	PUNCT
hjic-943	69	9	v	v	NOUN
hjic-943	69	10	,	,	PUNCT
hjic-943	69	11	a	a	PRON
hjic-943	69	12	,	,	PUNCT
hjic-943	69	13	x	x	NOUN
hjic-943	69	14	,	,	PUNCT
hjic-943	69	15	y	y	PROPN
hjic-943	69	16	)	)	PUNCT
hjic-943	69	17	,	,	PUNCT
hjic-943	69	18	where	where	SCONJ
hjic-943	69	19	v	v	NOUN
hjic-943	69	20	is	be	AUX
hjic-943	69	21	the	the	DET
hjic-943	69	22	vertex	vertex	NOUN
hjic-943	69	23	-	-	PUNCT
hjic-943	69	24	set	set	NOUN
hjic-943	69	25	,	,	PUNCT
hjic-943	69	26	a	a	PRON
hjic-943	69	27	is	be	AUX
hjic-943	69	28	the	the	DET
hjic-943	69	29	arc	arc	NOUN
hjic-943	69	30	-	-	PUNCT
hjic-943	69	31	set	set	NOUN
hjic-943	69	32	,	,	PUNCT
hjic-943	69	33	x	x	X
hjic-943	69	34	is	be	AUX
hjic-943	69	35	the	the	DET
hjic-943	69	36	entral).ce	entral).ce	NOUN
hjic-943	69	37	and	and	CCONJ
hjic-943	69	38	yis	yis	PRON
hjic-943	69	39	the	the	DET
hjic-943	69	40	exit	exit	NOUN
hjic-943	69	41	of	of	ADP
hjic-943	69	42	the	the	DET
hjic-943	69	43	graph	graph	NOUN
hjic-943	69	44	.	.	PUNCT
hjic-943	70	1	the	the	DET
hjic-943	70	2	representation	representation	NOUN
hjic-943	70	3	graph	graph	NOUN
hjic-943	70	4	satisfies	satisfy	VERB
hjic-943	70	5	the	the	DET
hjic-943	70	6	following	follow	VERB
hjic-943	70	7	properties	property	NOUN
hjic-943	70	8	:	:	PUNCT
hjic-943	70	9	1	1	X
hjic-943	70	10	.	.	PUNCT
hjic-943	70	11	each	each	DET
hjic-943	70	12	vertex	vertex	NOUN
hjic-943	70	13	x	x	X
hjic-943	70	14	e	e	NOUN
hjic-943	70	15	x	x	PUNCT
hjic-943	70	16	has	have	VERB
hjic-943	70	17	no	no	DET
hjic-943	70	18	in	in	NOUN
hjic-943	70	19	-	-	PUNCT
hjic-943	70	20	com	com	NOUN
hjic-943	70	21	~	~	PROPN
hjic-943	70	22	ng	ng	PROPN
hjic-943	70	23	arcs	arcs	PROPN
hjic-943	70	24	.	.	PUNCT
hjic-943	71	1	(	(	PUNCT
hjic-943	71	2	these	these	PRON
hjic-943	71	3	are	be	AUX
hjic-943	71	4	initial	initial	ADJ
hjic-943	71	5	vertices	vertex	NOUN
hjic-943	71	6	.	.	PUNCT
hjic-943	71	7	)	)	PUNCT
hjic-943	72	1	2	2	X
hjic-943	72	2	.	.	X
hjic-943	73	1	each	each	DET
hjic-943	73	2	vertex	vertex	NOUN
hjic-943	73	3	y	y	PROPN
hjic-943	73	4	e	e	PROPN
hjic-943	73	5	y	y	PROPN
hjic-943	73	6	has	have	VERB
hjic-943	73	7	no	no	DET
hjic-943	73	8	out	out	ADV
hjic-943	73	9	-	-	PUNCT
hjic-943	73	10	going	go	VERB
hjic-943	73	11	arcs	arc	NOUN
hjic-943	73	12	.	.	PUNCT
hjic-943	74	1	(	(	PUNCT
hjic-943	74	2	these	these	PRON
hjic-943	74	3	are	be	AUX
hjic-943	74	4	terminal	terminal	ADJ
hjic-943	74	5	vertices	vertex	NOUN
hjic-943	74	6	.	.	PUNCT
hjic-943	74	7	)	)	PUNCT
hjic-943	75	1	the	the	DET
hjic-943	75	2	representation	representation	NOUN
hjic-943	75	3	graph	graph	NOUN
hjic-943	75	4	may	may	AUX
hjic-943	75	5	be	be	AUX
hjic-943	75	6	regarded	regard	VERB
hjic-943	75	7	as	as	ADP
hjic-943	75	8	the	the	DET
hjic-943	75	9	flow	flow	NOUN
hjic-943	75	10	of	of	ADP
hjic-943	75	11	information	information	NOUN
hjic-943	75	12	in	in	ADP
hjic-943	75	13	the	the	DET
hjic-943	75	14	system	system	NOUN
hjic-943	75	15	as	as	SCONJ
hjic-943	75	16	it	it	PRON
hjic-943	75	17	expresses	express	VERB
hjic-943	75	18	the	the	DET
hjic-943	75	19	existence	existence	NOUN
hjic-943	75	20	of	of	ADP
hjic-943	75	21	functional	functional	ADJ
hjic-943	75	22	dependence	dependence	NOUN
hjic-943	75	23	among	among	ADP
hjic-943	75	24	variables	variable	NOUN
hjic-943	75	25	.	.	PUNCT
hjic-943	76	1	example	example	NOUN
hjic-943	76	2	1	1	NUM
hjic-943	76	3	.	.	X
hjic-943	77	1	consider	consider	VERB
hjic-943	77	2	the	the	DET
hjic-943	77	3	following	follow	VERB
hjic-943	77	4	system	system	NOUN
hjic-943	77	5	of	of	ADP
hjic-943	77	6	equations	equation	NOUN
hjic-943	77	7	:	:	PUNCT
hjic-943	77	8	yt	yt	NOUN
hjic-943	77	9	=	=	PUNCT
hjic-943	77	10	/i(xl"~t•u3	/i(xl"~t•u3	PROPN
hjic-943	77	11	)	)	PUNCT
hjic-943	77	12	(	(	PUNCT
hjic-943	77	13	6	6	X
hjic-943	77	14	)	)	PUNCT
hjic-943	78	1	yz	yz	NOUN
hjic-943	79	1	=	=	NOUN
hjic-943	79	2	=	=	SYM
hjic-943	79	3	f2(upu3	f2(upu3	PROPN
hjic-943	79	4	)	)	PUNCT
hjic-943	79	5	(	(	PUNCT
hjic-943	79	6	7	7	X
hjic-943	79	7	)	)	PUNCT
hjic-943	79	8	yj	yj	NOUN
hjic-943	79	9	=	=	SYM
hjic-943	79	10	f3(xz	f3(xz	PROPN
hjic-943	79	11	,	,	PUNCT
hjic-943	79	12	u3,u4	u3,u4	PROPN
hjic-943	79	13	)	)	PUNCT
hjic-943	79	14	(	(	PUNCT
hjic-943	79	15	8)	8)	NUM
hjic-943	79	16	u1	u1	NOUN
hjic-943	79	17	=	=	SYM
hjic-943	79	18	=	=	SYM
hjic-943	79	19	g1(x1,u2	g1(x1,u2	PROPN
hjic-943	79	20	}	}	PUNCT
hjic-943	79	21	(	(	PUNCT
hjic-943	79	22	9	9	NUM
hjic-943	79	23	)	)	PUNCT
hjic-943	79	24	"	"	PUNCT
hjic-943	79	25	2	2	NUM
hjic-943	79	26	=	=	SYM
hjic-943	79	27	8z(xl	8z(xl	NUM
hjic-943	79	28	,	,	PUNCT
hjic-943	79	29	x2,u3	x2,u3	PROPN
hjic-943	79	30	)	)	PUNCT
hjic-943	79	31	(	(	PUNCT
hjic-943	79	32	10	10	X
hjic-943	79	33	)	)	PUNCT
hjic-943	79	34	u3	u3	NOUN
hjic-943	79	35	=	=	NOUN
hjic-943	79	36	g3(u1	g3(u1	NOUN
hjic-943	79	37	)	)	PUNCT
hjic-943	79	38	(	(	PUNCT
hjic-943	79	39	11	11	NUM
hjic-943	79	40	)	)	PUNCT
hjic-943	79	41	~	~	PUNCT
hjic-943	80	1	arcs	arc	NOUN
hjic-943	80	2	of	of	ADP
hjic-943	80	3	a	a	DET
hjic-943	80	4	mengsr	mengsr	ADJ
hjic-943	80	5	-	-	PUNCT
hjic-943	80	6	type	type	NOUN
hjic-943	80	7	complete	complete	ADJ
hjic-943	80	8	linking	link	VERB
hjic-943	80	9	fig.l	fig.l	PROPN
hjic-943	80	10	representation	representation	NOUN
hjic-943	80	11	of	of	ADP
hjic-943	80	12	model	model	NOUN
hjic-943	80	13	in	in	ADP
hjic-943	80	14	example	example	NOUN
hjic-943	80	15	i	i	PRON
hjic-943	80	16	(	(	PUNCT
hjic-943	80	17	12	12	NUM
hjic-943	80	18	)	)	PUNCT
hjic-943	80	19	the	the	DET
hjic-943	80	20	representation	representation	NOUN
hjic-943	80	21	graph	graph	NOUN
hjic-943	80	22	of	of	ADP
hjic-943	80	23	the	the	DET
hjic-943	80	24	system	system	NOUN
hjic-943	80	25	above	above	ADV
hjic-943	80	26	is	be	AUX
hjic-943	80	27	shown	show	VERB
hjic-943	80	28	in	in	ADP
hjic-943	80	29	fig	fig	NOUN
hjic-943	80	30	.	.	PUNCT
hjic-943	81	1	i.	i.	PROPN
hjic-943	81	2	there	there	PRON
hjic-943	81	3	is	be	VERB
hjic-943	81	4	a	a	DET
hjic-943	81	5	generality	generality	NOUN
hjic-943	81	6	assumption	assumption	NOUN
hjic-943	81	7	(	(	PUNCT
hjic-943	81	8	abbreviated	abbreviate	VERB
hjic-943	81	9	by	by	ADP
hjic-943	81	10	ga	ga	PROPN
hjic-943	81	11	)	)	PUNCT
hjic-943	81	12	on	on	ADP
hjic-943	81	13	the	the	DET
hjic-943	81	14	functions.fi	functions.fi	NOUN
hjic-943	81	15	,	,	PUNCT
hjic-943	81	16	(	(	PUNCT
hjic-943	81	17	i	i	NOUN
hjic-943	81	18	=	=	NOUN
hjic-943	81	19	1	1	NUM
hjic-943	81	20	,	,	PUNCT
hjic-943	81	21	...	...	PUNCT
hjic-943	81	22	,	,	PUNCT
hjic-943	81	23	m	m	PROPN
hjic-943	81	24	)	)	PUNCT
hjic-943	81	25	and	and	CCONJ
hjic-943	81	26	gb	gb	PRON
hjic-943	81	27	(	(	PUNCT
hjic-943	81	28	k	k	NOUN
hjic-943	81	29	=	=	SYM
hjic-943	81	30	1	1	NUM
hjic-943	81	31	,	,	PUNCT
hjic-943	81	32	...	...	PUNCT
hjic-943	81	33	,	,	PUNCT
hjic-943	81	34	k	k	X
hjic-943	81	35	)	)	PUNCT
hjic-943	81	36	on	on	ADP
hjic-943	81	37	which	which	PRON
hjic-943	81	38	the	the	DET
hjic-943	81	39	graphical	graphical	ADJ
hjic-943	81	40	methods	method	NOUN
hjic-943	81	41	of	of	ADP
hjic-943	81	42	decomposition	decomposition	NOUN
hjic-943	81	43	are	be	AUX
hjic-943	81	44	based	base	VERB
hjic-943	81	45	which	which	PRON
hjic-943	81	46	is	be	AUX
hjic-943	81	47	stated	state	VERB
hjic-943	81	48	as	as	SCONJ
hjic-943	81	49	follows	follow	VERB
hjic-943	81	50	:	:	PUNCT
hjic-943	81	51	ga	ga	NOUN
hjic-943	81	52	:	:	PUNCT
hjic-943	81	53	let	let	VERB
hjic-943	81	54	.j	.j	VERB
hjic-943	81	55	'	'	PUNCT
hjic-943	81	56	be	be	AUX
hjic-943	81	57	the	the	DET
hjic-943	81	58	collection	collection	NOUN
hjic-943	81	59	of	of	ADP
hjic-943	81	60	all	all	DET
hjic-943	81	61	partial	partial	ADJ
hjic-943	81	62	derivatives	derivative	NOUN
hjic-943	81	63	of	of	ADP
hjic-943	81	64	.fi	.fi	PUNCT
hjic-943	81	65	and	and	CCONJ
hjic-943	81	66	gkthe	gkthe	DET
hjic-943	81	67	non	non	ADJ
hjic-943	81	68	-	-	ADJ
hjic-943	81	69	vanishing	vanishing	ADJ
hjic-943	81	70	elements	element	NOUN
hjic-943	81	71	of	of	ADP
hjic-943	81	72	.j	.j	PROPN
hjic-943	81	73	'	'	PUNCT
hjic-943	81	74	are	be	AUX
hjic-943	81	75	algebraically	algebraically	ADV
hjic-943	81	76	independent	independent	ADJ
hjic-943	81	77	over	over	ADP
hjic-943	81	78	the	the	DET
hjic-943	81	79	rational	rational	ADJ
hjic-943	81	80	number	number	NOUN
hjic-943	81	81	field	field	NOUN
hjic-943	81	82	.f	.f	NOUN
hjic-943	81	83	.	.	PUNCT
hjic-943	82	1	this	this	DET
hjic-943	82	2	assumption	assumption	NOUN
hjic-943	82	3	means	mean	NOUN
hjic-943	82	4	,	,	PUNCT
hjic-943	82	5	that	that	SCONJ
hjic-943	82	6	the	the	DET
hjic-943	82	7	non	non	ADJ
hjic-943	82	8	-	-	ADJ
hjic-943	82	9	vanishing	vanishing	ADJ
hjic-943	82	10	partial	partial	ADJ
hjic-943	82	11	derivatives	derivative	NOUN
hjic-943	82	12	of.fi	of.fi	ADV
hjic-943	82	13	and	and	CCONJ
hjic-943	82	14	gk	gk	PROPN
hjic-943	82	15	are	be	AUX
hjic-943	82	16	"	"	PUNCT
hjic-943	82	17	so	so	ADV
hjic-943	82	18	general	general	ADJ
hjic-943	82	19	"	"	PUNCT
hjic-943	82	20	,	,	PUNCT
hjic-943	82	21	that	that	SCONJ
hjic-943	82	22	they	they	PRON
hjic-943	82	23	do	do	AUX
hjic-943	82	24	not	not	PART
hjic-943	82	25	satisfy	satisfy	VERB
hjic-943	82	26	any	any	DET
hjic-943	82	27	polynomial	polynomial	ADJ
hjic-943	82	28	relation	relation	NOUN
hjic-943	82	29	with	with	ADP
hjic-943	82	30	integer	integer	PROPN
hjic-943	82	31	coefficients	coefficient	NOUN
hjic-943	82	32	.	.	PUNCT
hjic-943	83	1	a	a	DET
hjic-943	83	2	menger	menger	NOUN
hjic-943	83	3	-	-	PUNCT
hjic-943	83	4	type	type	NOUN
hjic-943	83	5	linking	linking	NOUN
hjic-943	83	6	[	[	X
hjic-943	83	7	9	9	NUM
hjic-943	83	8	]	]	PUNCT
hjic-943	83	9	from	from	ADP
hjic-943	83	10	x	x	PUNCT
hjic-943	83	11	to	to	ADP
hjic-943	83	12	y	y	PROPN
hjic-943	83	13	is	be	AUX
hjic-943	83	14	a	a	DET
hjic-943	83	15	set	set	NOUN
hjic-943	83	16	of	of	ADP
hjic-943	83	17	pair	pair	NOUN
hjic-943	83	18	-	-	PUNCT
hjic-943	83	19	wise	wise	ADJ
hjic-943	83	20	vertex	vertex	NOUN
hjic-943	83	21	-	-	PUNCT
hjic-943	83	22	disjoint	disjoint	NOUN
hjic-943	83	23	directed	direct	VERB
hjic-943	83	24	paths	path	NOUN
hjic-943	83	25	from	from	ADP
hjic-943	83	26	a	a	DET
hjic-943	83	27	vertex	vertex	NOUN
hjic-943	83	28	in	in	ADP
hjic-943	83	29	x	x	PUNCT
hjic-943	83	30	to	to	ADP
hjic-943	83	31	a	a	DET
hjic-943	83	32	vertex	vertex	NOUN
hjic-943	83	33	in	in	ADP
hjic-943	83	34	y.	y.	NOUN
hjic-943	83	35	the	the	DET
hjic-943	83	36	size	size	NOUN
hjic-943	83	37	of	of	ADP
hjic-943	83	38	a	a	DET
hjic-943	83	39	linking	linking	NOUN
hjic-943	83	40	is	be	AUX
hjic-943	83	41	the	the	DET
hjic-943	83	42	number	number	NOUN
hjic-943	83	43	of	of	ADP
hjic-943	83	44	directed	direct	VERB
hjic-943	83	45	paths	path	NOUN
hjic-943	83	46	from	from	ADP
hjic-943	83	47	x	x	PUNCT
hjic-943	83	48	to	to	ADP
hjic-943	83	49	y	y	PROPN
hjic-943	83	50	contained	contain	VERB
hjic-943	83	51	in	in	ADP
hjic-943	83	52	the	the	DET
hjic-943	83	53	linking	linking	NOUN
hjic-943	83	54	.	.	PUNCT
hjic-943	84	1	in	in	ADP
hjic-943	84	2	case	case	NOUN
hjic-943	84	3	!	!	PUNCT
hjic-943	84	4	xi	xi	X
hjic-943	84	5	=	=	PROPN
hjic-943	84	6	jyj	jyj	PROPN
hjic-943	84	7	,	,	PUNCT
hjic-943	84	8	(	(	PUNCT
hjic-943	84	9	m	m	NOUN
hjic-943	84	10	=	=	SYM
hjic-943	84	11	n	n	CCONJ
hjic-943	84	12	)	)	PUNCT
hjic-943	84	13	,	,	PUNCT
hjic-943	84	14	a	a	DET
hjic-943	84	15	linking	linking	NOUN
hjic-943	84	16	of	of	ADP
hjic-943	84	17	size	size	NOUN
hjic-943	84	18	lxi	lxi	NOUN
hjic-943	84	19	is	be	AUX
hjic-943	84	20	called	call	VERB
hjic-943	84	21	a	a	DET
hjic-943	84	22	complete	complete	ADJ
hjic-943	84	23	linking	linking	NOUN
hjic-943	84	24	.	.	PUNCT
hjic-943	85	1	the	the	DET
hjic-943	85	2	graphical	graphical	ADJ
hjic-943	85	3	condition	condition	NOUN
hjic-943	85	4	of	of	ADP
hjic-943	85	5	the	the	DET
hjic-943	85	6	'	'	PUNCT
hjic-943	85	7	structural	structural	ADJ
hjic-943	85	8	solvability	solvability	NOUN
hjic-943	85	9	is	be	AUX
hjic-943	85	10	then	then	ADV
hjic-943	85	11	the	the	DET
hjic-943	85	12	following	follow	VERB
hjic-943	85	13	:	:	PUNCT
hjic-943	85	14	linkage	linkage	NOUN
hjic-943	85	15	theorem	theorem	NOUN
hjic-943	85	16	[	[	X
hjic-943	85	17	9	9	NUM
hjic-943	85	18	]	]	PUNCT
hjic-943	85	19	:	:	PUNCT
hjic-943	85	20	assume	assume	VERB
hjic-943	85	21	ga	ga	PROPN
hjic-943	85	22	is	be	AUX
hjic-943	85	23	true	true	ADJ
hjic-943	85	24	.	.	PUNCT
hjic-943	86	1	a	a	DET
hjic-943	86	2	system	system	NOUN
hjic-943	86	3	of	of	ADP
hjic-943	86	4	equations	equation	NOUN
hjic-943	86	5	in	in	ADP
hjic-943	86	6	the	the	DET
hjic-943	86	7	standard	standard	ADJ
hjic-943	86	8	form	form	NOUN
hjic-943	86	9	is	be	AUX
hjic-943	86	10	structurally	structurally	ADV
hjic-943	86	11	solvable	solvable	ADJ
hjic-943	86	12	if	if	SCONJ
hjic-943	87	1	and	and	CCONJ
hjic-943	87	2	only	only	ADV
hjic-943	87	3	if	if	SCONJ
hjic-943	87	4	there	there	PRON
hjic-943	87	5	exists	exist	VERB
hjic-943	87	6	on	on	ADP
hjic-943	87	7	the	the	DET
hjic-943	87	8	representation	representation	NOUN
hjic-943	87	9	graph	graph	NOUN
hjic-943	87	10	a	a	DET
hjic-943	87	11	menger	menger	NOUN
hjic-943	87	12	-	-	PUNCT
hjic-943	87	13	type	type	NOUN
hjic-943	87	14	complete	complete	ADJ
hjic-943	87	15	linking	linking	NOUN
hjic-943	87	16	from	from	ADP
hjic-943	87	17	x	x	PUNCT
hjic-943	87	18	to	to	ADP
hjic-943	87	19	y.	y.	NOUN
hjic-943	87	20	in	in	ADP
hjic-943	87	21	rigorous	rigorous	ADJ
hjic-943	87	22	mathematical	mathematical	ADJ
hjic-943	87	23	sense	sense	NOUN
hjic-943	87	24	,	,	PUNCT
hjic-943	87	25	the	the	DET
hjic-943	87	26	structural	structural	ADJ
hjic-943	87	27	solvability	solvability	NOUN
hjic-943	87	28	and	and	CCONJ
hjic-943	87	29	the	the	DET
hjic-943	87	30	existence	existence	NOUN
hjic-943	87	31	of	of	ADP
hjic-943	87	32	the	the	DET
hjic-943	87	33	menger	menger	NOUN
hjic-943	87	34	-	-	PUNCT
hjic-943	87	35	type	type	NOUN
hjic-943	87	36	complete	complete	ADJ
hjic-943	87	37	linking	linking	NOUN
hjic-943	87	38	are	be	AUX
hjic-943	87	39	equivalent	equivalent	ADJ
hjic-943	87	40	under	under	ADP
hjic-943	87	41	the	the	DET
hjic-943	87	42	above	above	ADJ
hjic-943	87	43	generality	generality	NOUN
hjic-943	87	44	assumption	assumption	PROPN
hjic-943	87	45	ga	ga	PROPN
hjic-943	87	46	.	.	PUNCT
hjic-943	88	1	in	in	ADP
hjic-943	88	2	many	many	ADJ
hjic-943	88	3	cases	case	NOUN
hjic-943	88	4	,	,	PUNCT
hjic-943	88	5	however	however	ADV
hjic-943	88	6	,	,	PUNCT
hjic-943	88	7	it	it	PRON
hjic-943	88	8	is	be	AUX
hjic-943	88	9	difficult	difficult	ADJ
hjic-943	88	10	to	to	PART
hjic-943	88	11	check	check	VERB
hjic-943	88	12	the	the	DET
hjic-943	88	13	validity	validity	NOUN
hjic-943	88	14	of	of	ADP
hjic-943	88	15	this	this	DET
hjic-943	88	16	assumption	assumption	NOUN
hjic-943	88	17	and/or	and/or	CCONJ
hjic-943	88	18	the	the	DET
hjic-943	88	19	assumption	assumption	NOUN
hjic-943	88	20	does	do	AUX
hjic-943	88	21	not	not	PART
hjic-943	88	22	hold	hold	VERB
hjic-943	88	23	at	at	ADV
hjic-943	88	24	all	all	ADV
hjic-943	88	25	,	,	PUNCT
hjic-943	88	26	therefore	therefore	ADV
hjic-943	88	27	we	we	PRON
hjic-943	88	28	use	use	VERB
hjic-943	88	29	the	the	DET
hjic-943	88	30	property	property	NOUN
hjic-943	88	31	conditional	conditional	ADJ
hjic-943	88	32	structural	structural	ADJ
hjic-943	88	33	solvability	solvability	NOUN
hjic-943	88	34	as	as	SCONJ
hjic-943	88	35	follows	follow	VERB
hjic-943	88	36	.	.	PUNCT
hjic-943	89	1	a	a	DET
hjic-943	89	2	system	system	NOUN
hjic-943	89	3	of	of	ADP
hjic-943	89	4	standard	standard	ADJ
hjic-943	89	5	form	form	NOUN
hjic-943	89	6	equations	equation	NOUN
hjic-943	89	7	is	be	AUX
hjic-943	89	8	conditionally	conditionally	ADV
hjic-943	89	9	structurally	structurally	ADV
hjic-943	89	10	solvable	solvable	ADJ
hjic-943	89	11	if	if	SCONJ
hjic-943	89	12	there	there	PRON
hjic-943	89	13	exists	exist	VERB
hjic-943	89	14	a	a	DET
hjic-943	89	15	menger	menger	NOUN
hjic-943	89	16	-	-	PUNCT
hjic-943	89	17	type	type	NOUN
hjic-943	89	18	complete	complete	ADJ
hjic-943	89	19	linking	linking	NOUN
hjic-943	89	20	from	from	ADP
hjic-943	89	21	x	x	PUNCT
hjic-943	89	22	to	to	ADP
hjic-943	89	23	y	y	PROPN
hjic-943	89	24	on	on	ADP
hjic-943	89	25	the	the	DET
hjic-943	89	26	representation	representation	NOUN
hjic-943	89	27	graph	graph	NOUN
hjic-943	89	28	.	.	PUNCT
hjic-943	90	1	here	here	ADV
hjic-943	90	2	we	we	PRON
hjic-943	90	3	do	do	AUX
hjic-943	90	4	not	not	PART
hjic-943	90	5	take	take	VERB
hjic-943	90	6	into	into	ADP
hjic-943	90	7	account	account	NOUN
hjic-943	90	8	the	the	DET
hjic-943	90	9	generality	generality	NOUN
hjic-943	90	10	assumption	assumption	PROPN
hjic-943	90	11	ga	ga	PROPN
hjic-943	90	12	.	.	PUNCT
hjic-943	91	1	obviously	obviously	ADV
hjic-943	91	2	the	the	DET
hjic-943	91	3	conditional	conditional	ADJ
hjic-943	91	4	structural	structural	ADJ
hjic-943	91	5	solvability	solvability	NOUN
hjic-943	91	6	is	be	AUX
hjic-943	91	7	a	a	DET
hjic-943	91	8	necessary	necessary	ADJ
hjic-943	91	9	condition	condition	NOUN
hjic-943	91	10	.	.	PUNCT
hjic-943	92	1	of	of	ADP
hjic-943	92	2	structural	structural	ADJ
hjic-943	92	3	solvability	solvability	NOUN
hjic-943	92	4	.	.	PUNCT
hjic-943	93	1	in	in	ADP
hjic-943	93	2	further	further	ADJ
hjic-943	93	3	examples	example	NOUN
hjic-943	93	4	we	we	PRON
hjic-943	93	5	investigate	investigate	VERB
hjic-943	93	6	the	the	DET
hjic-943	93	7	conditional	conditional	ADJ
hjic-943	93	8	structural	structural	ADJ
hjic-943	93	9	solvability	solvability	NOUN
hjic-943	93	10	of	of	ADP
hjic-943	93	11	models	model	NOUN
hjic-943	93	12	.	.	PUNCT
hjic-943	94	1	example	example	NOUN
hjic-943	94	2	1	1	NUM
hjic-943	94	3	(	(	PUNCT
hjic-943	94	4	continued	continue	VERB
hjic-943	94	5	)	)	PUNCT
hjic-943	94	6	.	.	PUNCT
hjic-943	95	1	as	as	SCONJ
hjic-943	95	2	shown	show	VERB
hjic-943	95	3	in	in	ADP
hjic-943	95	4	fig.l	fig.l	PROPN
hjic-943	95	5	there	there	PRON
hjic-943	95	6	exists	exist	VERB
hjic-943	95	7	a	a	DET
hjic-943	95	8	menger	menger	NOUN
hjic-943	95	9	-	-	PUNCT
hjic-943	95	10	type	type	NOUN
hjic-943	95	11	complete	complete	ADJ
hjic-943	95	12	linking	linking	NOUN
hjic-943	95	13	{	{	PUNCT
hjic-943	95	14	xi	xi	PROPN
hjic-943	95	15	--7ytt	--7ytt	PROPN
hjic-943	95	16	x2	x2	PROPN
hjic-943	96	1	~	~	PUNCT
hjic-943	96	2	u2	u2	PROPN
hjic-943	96	3	~	~	PUNCT
hjic-943	96	4	ut	ut	PROPN
hjic-943	96	5	_	_	PROPN
hjic-943	96	6	,	,	PUNCT
hjic-943	96	7	.	.	PUNCT
hjic-943	97	1	u3	u3	PROPN
hjic-943	97	2	-t	-t	PUNCT
hjic-943	97	3	y2	y2	PROPN
hjic-943	97	4	,	,	PUNCT
hjic-943	97	5	x3	x3	PROPN
hjic-943	97	6	--7u4	--7u4	PROPN
hjic-943	97	7	--7	--7	NOUN
hjic-943	97	8	y3	y3	NOUN
hjic-943	97	9	}	}	PUNCT
hjic-943	97	10	on	on	ADP
hjic-943	97	11	the	the	DET
hjic-943	97	12	representation	representation	NOUN
hjic-943	97	13	63	63	NUM
hjic-943	97	14	graph	graph	NOUN
hjic-943	97	15	,	,	PUNCT
hjic-943	97	16	so	so	SCONJ
hjic-943	97	17	the	the	DET
hjic-943	97	18	system	system	NOUN
hjic-943	97	19	described	describe	VERB
hjic-943	97	20	in	in	ADP
hjic-943	97	21	example	example	NOUN
hjic-943	97	22	i	i	PRON
hjic-943	97	23	is	be	AUX
hjic-943	97	24	structurally	structurally	ADV
hjic-943	97	25	solvable	solvable	ADJ
hjic-943	97	26	under	under	ADP
hjic-943	97	27	ga	ga	PROPN
hjic-943	97	28	.	.	PROPN
hjic-943	97	29	from	from	ADP
hjic-943	97	30	the	the	DET
hjic-943	97	31	viewpoint	viewpoint	NOUN
hjic-943	97	32	of	of	ADP
hjic-943	97	33	structural	structural	ADJ
hjic-943	97	34	solvability	solvability	NOUN
hjic-943	97	35	two	two	NUM
hjic-943	97	36	types	type	NOUN
hjic-943	97	37	of	of	ADP
hjic-943	97	38	model	model	NOUN
hjic-943	97	39	decompositions	decomposition	NOUN
hjic-943	97	40	can	can	AUX
hjic-943	97	41	be	be	AUX
hjic-943	97	42	defined	define	VERB
hjic-943	97	43	and	and	CCONJ
hjic-943	97	44	constructed	construct	VERB
hjic-943	97	45	using	use	VERB
hjic-943	97	46	the	the	DET
hjic-943	97	47	representation	representation	NOUN
hjic-943	97	48	graph	graph	NOUN
hjic-943	97	49	.	.	PUNCT
hjic-943	98	1	the	the	DET
hjic-943	98	2	goal	goal	NOUN
hjic-943	98	3	of	of	ADP
hjic-943	98	4	these	these	DET
hjic-943	98	5	decompositions	decomposition	NOUN
hjic-943	98	6	is	be	AUX
hjic-943	98	7	to	to	PART
hjic-943	98	8	obtain	obtain	VERB
hjic-943	98	9	the	the	DET
hjic-943	98	10	sub	sub	NOUN
hjic-943	98	11	-	-	NOUN
hjic-943	98	12	systems	system	NOUN
hjic-943	98	13	of	of	ADP
hjic-943	98	14	a	a	DET
hjic-943	98	15	model	model	NOUN
hjic-943	98	16	and	and	CCONJ
hjic-943	98	17	to	to	PART
hjic-943	98	18	determine	determine	VERB
hjic-943	98	19	a	a	DET
hjic-943	98	20	successful	successful	ADJ
hjic-943	98	21	way	way	NOUN
hjic-943	98	22	for	for	ADP
hjic-943	98	23	solving	solve	VERB
hjic-943	98	24	the	the	DET
hjic-943	98	25	model	model	NOUN
hjic-943	98	26	equations	equation	NOUN
hjic-943	98	27	.	.	PUNCT
hjic-943	99	1	representation	representation	NOUN
hjic-943	99	2	of	of	ADP
hjic-943	99	3	dynamic	dynamic	ADJ
hjic-943	99	4	process	process	NOUN
hjic-943	99	5	models	model	NOUN
hjic-943	99	6	we	we	PRON
hjic-943	99	7	can	can	AUX
hjic-943	99	8	adapt	adapt	VERB
hjic-943	99	9	the	the	DET
hjic-943	99	10	graphical	graphical	ADJ
hjic-943	99	11	techniques	technique	NOUN
hjic-943	99	12	described	describe	VERB
hjic-943	99	13	above	above	ADV
hjic-943	99	14	to	to	ADP
hjic-943	99	15	dab	dab	NOUN
hjic-943	99	16	-	-	PUNCT
hjic-943	99	17	system	system	NOUN
hjic-943	99	18	,	,	PUNCT
hjic-943	99	19	as	as	ADV
hjic-943	99	20	well	well	ADV
hjic-943	99	21	[	[	X
hjic-943	99	22	12	12	NUM
hjic-943	99	23	]	]	PUNCT
hjic-943	99	24	.	.	PUNCT
hjic-943	100	1	an	an	DET
hjic-943	100	2	ordinary	ordinary	ADJ
hjic-943	100	3	differential	differential	ADJ
hjic-943	100	4	equation	equation	NOUN
hjic-943	100	5	of	of	ADP
hjic-943	100	6	a	a	DET
hjic-943	100	7	dae	dae	NOUN
hjic-943	100	8	system	system	NOUN
hjic-943	100	9	can	can	AUX
hjic-943	100	10	be	be	AUX
hjic-943	100	11	described	describe	VERB
hjic-943	100	12	by	by	ADP
hjic-943	100	13	the	the	DET
hjic-943	100	14	following	follow	VERB
hjic-943	100	15	equation	equation	NOUN
hjic-943	100	16	:	:	PUNCT
hjic-943	100	17	(	(	PUNCT
hjic-943	100	18	13	13	NUM
hjic-943	100	19	)	)	PUNCT
hjic-943	100	20	here	here	ADV
hjic-943	100	21	x	x	PUNCT
hjic-943	100	22	denotes	denote	VERB
hjic-943	100	23	an	an	DET
hjic-943	100	24	arbitrary	arbitrary	ADJ
hjic-943	100	25	variable	variable	NOUN
hjic-943	100	26	depending	depend	VERB
hjic-943	100	27	on	on	ADP
hjic-943	100	28	time	time	NOUN
hjic-943	100	29	,	,	PUNCT
hjic-943	100	30	x	x	X
hjic-943	100	31	'	'	PUNCT
hjic-943	100	32	denotes	denote	VERB
hjic-943	100	33	the	the	DET
hjic-943	100	34	derivative	derivative	NOUN
hjic-943	100	35	of	of	ADP
hjic-943	100	36	x	x	PUNCT
hjic-943	100	37	with	with	ADP
hjic-943	100	38	respect	respect	NOUN
hjic-943	100	39	to	to	ADP
hjic-943	100	40	time	time	NOUN
hjic-943	100	41	and	and	CCONJ
hjic-943	100	42	xj	xj	PROPN
hjic-943	100	43	,	,	PUNCT
hjic-943	100	44	...	...	PUNCT
hjic-943	100	45	,	,	PUNCT
hjic-943	100	46	xn	xn	PROPN
hjic-943	100	47	are	be	AUX
hjic-943	100	48	those	those	DET
hjic-943	100	49	variables	variable	NOUN
hjic-943	100	50	which	which	PRON
hjic-943	100	51	have	have	VERB
hjic-943	100	52	effect	effect	NOUN
hjic-943	100	53	on	on	ADP
hjic-943	100	54	variable	variable	ADJ
hjic-943	100	55	x	x	NOUN
hjic-943	100	56	'	'	PUNCT
hjic-943	100	57	in	in	ADP
hjic-943	100	58	the	the	DET
hjic-943	100	59	model	model	NOUN
hjic-943	100	60	.	.	PUNCT
hjic-943	101	1	the	the	DET
hjic-943	101	2	variable	variable	ADJ
hjic-943	101	3	x	x	PROPN
hjic-943	101	4	of	of	ADP
hjic-943	101	5	the	the	DET
hjic-943	101	6	above	above	ADJ
hjic-943	101	7	differential	differential	ADJ
hjic-943	101	8	equation	equation	NOUN
hjic-943	101	9	is	be	AUX
hjic-943	101	10	usually	usually	ADV
hjic-943	101	11	determined	determine	VERB
hjic-943	101	12	using	use	VERB
hjic-943	101	13	a	a	DET
hjic-943	101	14	numerical	numerical	ADJ
hjic-943	101	15	integration	integration	NOUN
hjic-943	101	16	method	method	NOUN
hjic-943	101	17	:	:	PUNCT
hjic-943	101	18	(	(	PUNCT
hjic-943	101	19	14	14	NUM
hjic-943	101	20	)	)	PUNCT
hjic-943	101	21	in	in	ADP
hjic-943	101	22	dab	dab	NOUN
hjic-943	101	23	systems	system	NOUN
hjic-943	101	24	there	there	PRON
hjic-943	101	25	are	be	VERB
hjic-943	101	26	two	two	NUM
hjic-943	101	27	types	type	NOUN
hjic-943	101	28	of	of	ADP
hjic-943	101	29	variables	variable	NOUN
hjic-943	101	30	.	.	PUNCT
hjic-943	102	1	differential	differential	ADJ
hjic-943	102	2	variables	variable	NOUN
hjic-943	102	3	are	be	AUX
hjic-943	102	4	the	the	DET
hjic-943	102	5	variables	variable	NOUN
hjic-943	102	6	with	with	ADP
hjic-943	102	7	their	their	PRON
hjic-943	102	8	time	time	NOUN
hjic-943	102	9	derivative	derivative	ADJ
hjic-943	102	10	present	present	NOUN
hjic-943	102	11	in	in	ADP
hjic-943	102	12	the	the	DET
hjic-943	102	13	model	model	NOUN
hjic-943	102	14	.	.	PUNCT
hjic-943	103	1	variables	variable	NOUN
hjic-943	103	2	which	which	PRON
hjic-943	103	3	do	do	AUX
hjic-943	103	4	not	not	PART
hjic-943	103	5	have	have	VERB
hjic-943	103	6	their	their	PRON
hjic-943	103	7	time	time	NOUN
hjic-943	103	8	derivative	derivative	ADJ
hjic-943	103	9	present	present	NOUN
hjic-943	103	10	are	be	AUX
hjic-943	103	11	called	call	VERB
hjic-943	103	12	algebrau	algebrau	ADJ
hjic-943	103	13	variables	variable	NOUN
hjic-943	103	14	.	.	PUNCT
hjic-943	104	1	the	the	DET
hjic-943	104	2	derivative	derivative	ADJ
hjic-943	104	3	x	x	NOUN
hjic-943	104	4	'	'	PUNCT
hjic-943	104	5	is	be	AUX
hjic-943	104	6	called	call	VERB
hjic-943	104	7	derivarirt	derivarirt	NOUN
hjic-943	104	8	.	.	PUNCT
hjic-943	104	9	'	'	PUNCT
hjic-943	105	1	(	(	PUNCT
hjic-943	105	2	velocity	velocity	NOUN
hjic-943	105	3	)	)	PUNCT
hjic-943	105	4	variable	variable	NOUN
hjic-943	105	5	.	.	PUNCT
hjic-943	106	1	a	a	DET
hjic-943	106	2	system	system	NOUN
hjic-943	106	3	of	of	ADP
hjic-943	106	4	equations	equation	NOUN
hjic-943	106	5	including	include	VERB
hjic-943	106	6	also	also	ADV
hjic-943	106	7	differential	differential	ADJ
hjic-943	106	8	equations	equation	NOUN
hjic-943	106	9	,	,	PUNCT
hjic-943	106	10	can	can	AUX
hjic-943	106	11	be	be	AUX
hjic-943	106	12	represented	represent	VERB
hjic-943	106	13	by	by	ADP
hjic-943	106	14	a	a	DET
hjic-943	106	15	dynamic	dynamic	ADJ
hjic-943	106	16	graph	graph	NOUN
hjic-943	106	17	.	.	PUNCT
hjic-943	107	1	a	a	DET
hjic-943	107	2	dynamic	dynamic	ADJ
hjic-943	107	3	graph	graph	NOUN
hjic-943	107	4	·	·	PUNCT
hjic-943	107	5	is	be	AUX
hjic-943	107	6	a	a	DET
hjic-943	107	7	sequence	sequence	NOUN
hjic-943	107	8	of	of	ADP
hjic-943	107	9	static	static	ADJ
hjic-943	107	10	graphs	graph	NOUN
hjic-943	107	11	corresponding	correspond	VERB
hjic-943	107	12	to	to	ADP
hjic-943	107	13	each	each	DET
hjic-943	107	14	time	time	NOUN
hjic-943	107	15	step	step	NOUN
hjic-943	107	16	of	of	ADP
hjic-943	107	17	integration	integration	NOUN
hjic-943	107	18	.	.	PUNCT
hjic-943	108	1	on	on	ADP
hjic-943	108	2	a	a	DET
hjic-943	108	3	dynamic	dynamic	ADJ
hjic-943	108	4	graph	graph	NOUN
hjic-943	108	5	there	there	PRON
hjic-943	108	6	are	be	VERB
hjic-943	108	7	direct	direct	ADJ
hjic-943	108	8	arcs	arcs	NOUN
hjic-943	108	9	attached	attach	VERB
hjic-943	108	10	from	from	ADP
hjic-943	108	11	the	the	DET
hjic-943	108	12	previous	previous	ADJ
hjic-943	108	13	static	static	ADJ
hjic-943	108	14	graph	graph	NOUN
hjic-943	108	15	to	to	ADP
hjic-943	108	16	succeeding	succeed	VERB
hjic-943	108	17	static	static	ADJ
hjic-943	108	18	graph	graph	NOUN
hjic-943	108	19	corresponding	correspond	VERB
hjic-943	108	20	to	to	ADP
hjic-943	108	21	the	the	DET
hjic-943	108	22	method	method	NOUN
hjic-943	108	23	for	for	ADP
hjic-943	108	24	solving	solve	VERB
hjic-943	108	25	ordinary	ordinary	ADJ
hjic-943	108	26	differential	differential	ADJ
hjic-943	108	27	equations	equation	NOUN
hjic-943	108	28	.	.	PUNCT
hjic-943	109	1	in	in	SCONJ
hjic-943	109	2	case	case	NOUN
hjic-943	109	3	of	of	ADP
hjic-943	109	4	an	an	DET
hjic-943	109	5	explicit	explicit	ADJ
hjic-943	109	6	method	method	NOUN
hjic-943	109	7	for	for	ADP
hjic-943	109	8	solving	solve	VERB
hjic-943	109	9	ordinary	ordinary	ADJ
hjic-943	109	10	differential	differential	ADJ
hjic-943	109	11	equations	equation	NOUN
hjic-943	109	12	the	the	DET
hjic-943	109	13	value	value	NOUN
hjic-943	109	14	of	of	ADP
hjic-943	109	15	a	a	DET
hjic-943	109	16	differential	differential	ADJ
hjic-943	109	17	variable	variable	NOUN
hjic-943	109	18	at	at	ADP
hjic-943	109	19	a	a	DET
hjic-943	109	20	given	give	VERB
hjic-943	109	21	time	time	NOUN
hjic-943	109	22	is	be	AUX
hjic-943	109	23	computed	compute	VERB
hjic-943	109	24	using	use	VERB
hjic-943	109	25	the	the	DET
hjic-943	109	26	corresponding	corresponding	ADJ
hjic-943	109	27	differential	differential	NOUN
hjic-943	109	28	value	value	NOUN
hjic-943	109	29	and	and	CCONJ
hjic-943	109	30	its	its	PRON
hjic-943	109	31	value	value	NOUN
hjic-943	109	32	at	at	ADP
hjic-943	109	33	previous	previous	ADJ
hjic-943	109	34	time	time	NOUN
hjic-943	109	35	,	,	PUNCT
hjic-943	109	36	for	for	ADP
hjic-943	109	37	example	example	NOUN
hjic-943	109	38	.	.	PUNCT
hjic-943	110	1	therefore	therefore	ADV
hjic-943	110	2	if	if	SCONJ
hjic-943	110	3	there	there	PRON
hjic-943	110	4	is	be	VERB
hjic-943	110	5	an	an	DET
hjic-943	110	6	ordinary	ordinary	ADJ
hjic-943	110	7	differe~~~~~	differe~~~~~	NOUN
hjic-943	110	8	equation	equation	NOUN
hjic-943	110	9	x	x	NOUN
hjic-943	110	10	'	'	PUNCT
hjic-943	110	11	=	=	SYM
hjic-943	110	12	f	f	PROPN
hjic-943	110	13	(	(	PUNCT
hjic-943	110	14	xt	xt	PROPN
hjic-943	110	15	.	.	PUNCT
hjic-943	110	16	....	....	PUNCT
hjic-943	111	1	xn	xn	X
hjic-943	111	2	)	)	PUNCT
hjic-943	111	3	in	in	ADP
hjic-943	111	4	the	the	DET
hjic-943	111	5	model	model	NOUN
hjic-943	111	6	,	,	PUNCT
hjic-943	111	7	we	we	PRON
hjic-943	111	8	can	can	AUX
hjic-943	111	9	rewnte	rewnte	VERB
hjic-943	111	10	tt	tt	PRON
hjic-943	111	11	into	into	ADP
hjic-943	111	12	the	the	DET
hjic-943	111	13	following	following	ADJ
hjic-943	111	14	standard	standard	ADJ
hjic-943	111	15	fonn	fonn	NOUN
hjic-943	111	16	:	:	PUNCT
hjic-943	111	17	x	x	SYM
hjic-943	111	18	=	=	VERB
hjic-943	111	19	jx	jx	NOUN
hjic-943	111	20	'	'	PUNCT
hjic-943	111	21	(	(	PUNCT
hjic-943	111	22	15	15	NUM
hjic-943	111	23	)	)	PUNCT
hjic-943	111	24	(	(	PUNCT
hjic-943	111	25	16	16	NUM
hjic-943	111	26	)	)	PUNCT
hjic-943	111	27	the	the	DET
hjic-943	111	28	representation	representation	NOUN
hjic-943	111	29	graph	graph	NOUN
hjic-943	111	30	corresponding	correspond	VERB
hjic-943	111	31	to	to	ADP
hjic-943	111	32	equations	equation	NOUN
hjic-943	111	33	(	(	PUNCT
hjic-943	111	34	15	15	NUM
hjic-943	111	35	)	)	PUNCT
hjic-943	111	36	and	and	CCONJ
hjic-943	111	37	(	(	PUNCT
hjic-943	111	38	16	16	NUM
hjic-943	111	39	)	)	PUNCT
hjic-943	111	40	is	be	AUX
hjic-943	111	41	shown	show	VERB
hjic-943	111	42	in	in	ADP
hjic-943	111	43	fig.2	fig.2	PROPN
hjic-943	111	44	.	.	PUNCT
hjic-943	112	1	it	it	PRON
hjic-943	112	2	can	can	AUX
hjic-943	112	3	be	be	AUX
hjic-943	112	4	~n	~n	NUM
hjic-943	112	5	that	that	SCONJ
hjic-943	112	6	there	there	PRON
hjic-943	112	7	are	be	VERB
hjic-943	112	8	vertices	vertex	NOUN
hjic-943	112	9	on	on	ADP
hjic-943	112	10	the	the	DET
hjic-943	112	11	static	static	ADJ
hjic-943	112	12	graphs	graph	NOUN
hjic-943	112	13	refemng	refemng	VERB
hjic-943	112	14	to	to	ADP
hjic-943	112	15	the	the	DET
hjic-943	112	16	differential	differential	ADJ
hjic-943	112	17	variable	variable	NOUN
hjic-943	112	18	x	x	NOUN
hjic-943	112	19	,	,	PUNCT
hjic-943	112	20	the	the	DET
hjic-943	112	21	derivative	derivative	ADJ
hjic-943	112	22	variable	variable	NOUN
hjic-943	112	23	x	x	NOUN
hjic-943	112	24	'	'	PUNCT
hjic-943	112	25	and	and	CCONJ
hjic-943	112	26	the	the	DET
hjic-943	112	27	variables	variable	NOUN
hjic-943	112	28	xh	xh	PROPN
hjic-943	112	29	...	...	PUNCT
hjic-943	112	30	•	•	NUM
hjic-943	112	31	x11	x11	NOUN
hjic-943	112	32	occurring	occur	VERB
hjic-943	112	33	in	in	ADP
hjic-943	112	34	eq	eq	ADP
hjic-943	112	35	.	.	PUNCT
hjic-943	113	1	(	(	PUNCT
hjic-943	113	2	16	16	NUM
hjic-943	113	3	)	)	PUNCT
hjic-943	113	4	.	.	PUNCT
hjic-943	114	1	direct	direct	ADJ
hjic-943	114	2	arcs	arcs	NOUN
hjic-943	114	3	attached	attach	VERB
hjic-943	114	4	to	to	ADP
hjic-943	114	5	static	static	ADJ
hjic-943	114	6	graphs	graph	NOUN
hjic-943	114	7	at	at	ADP
hjic-943	114	8	time	time	NOUN
hjic-943	114	9	step	step	NOUN
hjic-943	114	10	t	t	PROPN
hjic-943	114	11	and	and	CCONJ
hjic-943	114	12	t+	t+	NOUN
hjic-943	114	13	1	1	NUM
hjic-943	114	14	correspond	correspond	NOUN
hjic-943	114	15	to	to	ADP
hjic-943	114	16	the	the	DET
hjic-943	114	17	applied	apply	VERB
hjic-943	114	18	euler	euler	NOUN
hjic-943	114	19	or	or	CCONJ
hjic-943	114	20	oth~	oth~	NOUN
hjic-943	114	21	expli	expli	NOUN
hjic-943	114	22	~	~	PUNCT
hjic-943	114	23	it	it	PRON
hjic-943	114	24	one·step	one·step	NOUN
hjic-943	114	25	method	method	NOUN
hjic-943	114	26	for	for	ADP
hjic-943	114	27	solving	solve	VERB
hjic-943	114	28	ordinary	ordinary	ADJ
hjic-943	114	29	d1fferenual	d1fferenual	ADJ
hjic-943	114	30	equations	equation	NOUN
hjic-943	114	31	.	.	PUNCT
hjic-943	115	1	64	64	NUM
hjic-943	115	2	t+1	t+1	NUM
hjic-943	115	3	--~------------r-~---------~'~	--~------------r-~---------~'~	PROPN
hjic-943	115	4	~/	~/	ADJ
hjic-943	115	5	.	.	PUNCT
hjic-943	115	6	'	'	PUNCT
hjic-943	116	1	"	"	PUNCT
hjic-943	116	2	.	.	PUNCT
hjic-943	117	1	,	,	PUNCT
hjic-943	117	2	..	..	PUNCT
hjic-943	118	1	:>	:>	X
hjic-943	118	2	:	:	PUNCT
hjic-943	118	3	-r	-r	PUNCT
hjic-943	118	4	t>{/	t>{/	PROPN
hjic-943	118	5	...	...	PUNCT
hjic-943	118	6	!	!	PUNCT
hjic-943	119	1	fig.2	fig.2	NOUN
hjic-943	119	2	representation	representation	NOUN
hjic-943	119	3	of	of	ADP
hjic-943	119	4	the	the	DET
hjic-943	119	5	structure	structure	NOUN
hjic-943	119	6	of	of	ADP
hjic-943	119	7	an	an	DET
hjic-943	119	8	ordinary	ordinary	ADJ
hjic-943	119	9	differential	differential	ADJ
hjic-943	119	10	equation	equation	NOUN
hjic-943	119	11	by	by	ADP
hjic-943	119	12	dynamic	dynamic	ADJ
hjic-943	119	13	graph	graph	NOUN
hjic-943	119	14	standard	standard	ADJ
hjic-943	119	15	form	form	NOUN
hjic-943	119	16	and	and	CCONJ
hjic-943	119	17	the	the	DET
hjic-943	119	18	reduced	reduce	VERB
hjic-943	119	19	graph	graph	NOUN
hjic-943	119	20	the	the	DET
hjic-943	119	21	form	form	NOUN
hjic-943	119	22	of	of	ADP
hjic-943	119	23	the	the	DET
hjic-943	119	24	representation	representation	NOUN
hjic-943	119	25	graph	graph	NOUN
hjic-943	119	26	for	for	ADP
hjic-943	119	27	dae	dae	NOUN
hjic-943	119	28	system	system	NOUN
hjic-943	119	29	models	model	NOUN
hjic-943	119	30	suitable	suitable	ADJ
hjic-943	119	31	for	for	ADP
hjic-943	119	32	.structural	.structural	ADJ
hjic-943	119	33	solvability	solvability	NOUN
hjic-943	119	34	analysis	analysis	NOUN
hjic-943	119	35	is	be	AUX
hjic-943	119	36	developed	develop	VERB
hjic-943	119	37	in	in	ADP
hjic-943	119	38	steps	step	NOUN
hjic-943	119	39	performed	perform	VERB
hjic-943	119	40	sequentially	sequentially	ADV
hjic-943	119	41	.	.	PUNCT
hjic-943	120	1	the	the	DET
hjic-943	120	2	first	first	ADJ
hjic-943	120	3	step	step	NOUN
hjic-943	120	4	for	for	ADP
hjic-943	120	5	investigation	investigation	NOUN
hjic-943	120	6	of	of	ADP
hjic-943	120	7	a	a	DET
hjic-943	120	8	dynamic	dynamic	ADJ
hjic-943	120	9	process	process	NOUN
hjic-943	120	10	model	model	NOUN
hjic-943	120	11	by	by	ADP
hjic-943	120	12	the	the	DET
hjic-943	120	13	graph	graph	NOUN
hjic-943	120	14	theoretical	theoretical	ADJ
hjic-943	120	15	technique	technique	NOUN
hjic-943	120	16	is	be	AUX
hjic-943	120	17	to	to	PART
hjic-943	120	18	rewrite	rewrite	VERB
hjic-943	120	19	·	·	PUNCT
hjic-943	120	20	the	the	DET
hjic-943	120	21	model	model	NOUN
hjic-943	120	22	into	into	ADP
hjic-943	120	23	the	the	DET
hjic-943	120	24	standard	standard	ADJ
hjic-943	120	25	form	form	NOUN
hjic-943	120	26	(	(	PUNCT
hjic-943	120	27	see	see	VERB
hjic-943	120	28	eqs	eqs	PROPN
hjic-943	120	29	.	.	PUNCT
hjic-943	121	1	(	(	PUNCT
hjic-943	121	2	1)-(2	1)-(2	NUM
hjic-943	121	3	)	)	PUNCT
hjic-943	121	4	and	and	CCONJ
hjic-943	121	5	(	(	PUNCT
hjic-943	121	6	15)-(16	15)-(16	NOUN
hjic-943	121	7	)	)	PUNCT
hjic-943	121	8	)	)	PUNCT
hjic-943	121	9	.	.	PUNCT
hjic-943	122	1	the	the	DET
hjic-943	122	2	second	second	ADJ
hjic-943	122	3	step	step	NOUN
hjic-943	122	4	is	be	AUX
hjic-943	122	5	the	the	DET
hjic-943	122	6	assignment	assignment	NOUN
hjic-943	122	7	of	of	ADP
hjic-943	122	8	types	type	NOUN
hjic-943	122	9	to	to	PART
hjic-943	122	10	vertices	vertex	NOUN
hjic-943	122	11	in	in	ADP
hjic-943	122	12	the	the	DET
hjic-943	122	13	representation	representation	NOUN
hjic-943	122	14	graph	graph	NOUN
hjic-943	122	15	[	[	X
hjic-943	122	16	5	5	NUM
hjic-943	122	17	]	]	PUNCT
hjic-943	122	18	.	.	PUNCT
hjic-943	123	1	the	the	DET
hjic-943	123	2	important	important	ADJ
hjic-943	123	3	types	type	NOUN
hjic-943	123	4	of	of	ADP
hjic-943	123	5	vertices	vertex	NOUN
hjic-943	123	6	corresponding	correspond	VERB
hjic-943	123	7	to	to	ADP
hjic-943	123	8	the	the	DET
hjic-943	123	9	model	model	NOUN
hjic-943	123	10	specification	specification	NOUN
hjic-943	123	11	are	be	AUX
hjic-943	123	12	the	the	DET
hjic-943	123	13	following	follow	VERB
hjic-943	123	14	:	:	PUNCT
hjic-943	124	1	•	•	ADP
hjic-943	124	2	<	<	X
hjic-943	124	3	s	s	X
hjic-943	124	4	>	>	X
hjic-943	124	5	(	(	PUNCT
hjic-943	124	6	set)-type	set)-type	NOUN
hjic-943	124	7	variables	variable	NOUN
hjic-943	124	8	these	these	PRON
hjic-943	124	9	represent	represent	VERB
hjic-943	124	10	variables	variable	NOUN
hjic-943	124	11	,	,	PUNCT
hjic-943	124	12	which	which	PRON
hjic-943	124	13	are	be	AUX
hjic-943	124	14	assigned	assign	VERB
hjic-943	124	15	to	to	ADP
hjic-943	124	16	the	the	DET
hjic-943	124	17	specified	specify	VERB
hjic-943	124	18	given	give	VERB
hjic-943	124	19	values	value	NOUN
hjic-943	124	20	.	.	PUNCT
hjic-943	125	1	these	these	DET
hjic-943	125	2	variables	variable	NOUN
hjic-943	125	3	require	require	VERB
hjic-943	125	4	no	no	DET
hjic-943	125	5	computation	computation	NOUN
hjic-943	125	6	and	and	CCONJ
hjic-943	125	7	are	be	AUX
hjic-943	125	8	present	present	ADJ
hjic-943	125	9	in	in	ADP
hjic-943	125	10	the	the	DET
hjic-943	125	11	specification	specification	NOUN
hjic-943	125	12	associated	associate	VERB
hjic-943	125	13	to	to	ADP
hjic-943	125	14	the	the	DET
hjic-943	125	15	process	process	NOUN
hjic-943	125	16	model	model	NOUN
hjic-943	125	17	.	.	PUNCT
hjic-943	126	1	the	the	DET
hjic-943	126	2	type	type	NOUN
hjic-943	126	3	<	<	X
hjic-943	126	4	s	s	X
hjic-943	126	5	>	>	X
hjic-943	126	6	is	be	AUX
hjic-943	126	7	usually	usually	ADV
hjic-943	126	8	assigned	assign	VERB
hjic-943	126	9	to	to	ADP
hjic-943	126	10	initial	initial	ADJ
hjic-943	126	11	vertices	vertex	NOUN
hjic-943	126	12	of	of	ADP
hjic-943	126	13	the	the	DET
hjic-943	126	14	representation	representation	NOUN
hjic-943	126	15	graph	graph	NOUN
hjic-943	126	16	.	.	PUNCT
hjic-943	127	1	in	in	ADP
hjic-943	127	2	case	case	NOUN
hjic-943	127	3	of	of	ADP
hjic-943	127	4	dynamic	dynamic	ADJ
hjic-943	127	5	representation	representation	NOUN
hjic-943	127	6	graph	graph	NOUN
hjic-943	127	7	we	we	PRON
hjic-943	127	8	can	can	AUX
hjic-943	127	9	assume	assume	VERB
hjic-943	127	10	an	an	DET
hjic-943	127	11	explicit	explicit	ADJ
hjic-943	127	12	euler	euler	NOUN
hjic-943	127	13	method	method	NOUN
hjic-943	127	14	(	(	PUNCT
hjic-943	127	15	or	or	CCONJ
hjic-943	127	16	another	another	DET
hjic-943	127	17	one­	one­	NOUN
hjic-943	127	18	step	step	NOUN
hjic-943	127	19	explicit	explicit	ADJ
hjic-943	127	20	method	method	NOUN
hjic-943	127	21	)	)	PUNCT
hjic-943	127	22	for	for	ADP
hjic-943	127	23	solving	solve	VERB
hjic-943	127	24	the	the	DET
hjic-943	127	25	differential	differential	ADJ
hjic-943	127	26	equations	equation	NOUN
hjic-943	127	27	.	.	PUNCT
hjic-943	128	1	therefore	therefore	ADV
hjic-943	128	2	the	the	DET
hjic-943	128	3	differential	differential	ADJ
hjic-943	128	4	variables	variable	NOUN
hjic-943	128	5	wm	wm	AUX
hjic-943	128	6	be	be	AUX
hjic-943	128	7	labeled	label	VERB
hjic-943	128	8	by	by	ADP
hjic-943	128	9	type	type	NOUN
hjic-943	128	10	<	<	X
hjic-943	128	11	s	s	X
hjic-943	128	12	>	>	X
hjic-943	128	13	because	because	SCONJ
hjic-943	128	14	their	their	PRON
hjic-943	128	15	initial	initial	ADJ
hjic-943	128	16	vaiue	vaiue	NOUN
hjic-943	128	17	can	can	AUX
hjic-943	128	18	be	be	AUX
hjic-943	128	19	obtained	obtain	VERB
hjic-943	128	20	from	from	ADP
hjic-943	128	21	the	the	DET
hjic-943	128	22	initial	initial	ADJ
hjic-943	128	23	conditions	condition	NOUN
hjic-943	128	24	then	then	ADV
hjic-943	128	25	their	their	PRON
hjic-943	128	26	values	value	NOUN
hjic-943	128	27	can	can	AUX
hjic-943	128	28	be	be	AUX
hjic-943	128	29	calculated	calculate	VERB
hjic-943	128	30	step	step	NOUN
hjic-943	128	31	by	by	ADP
hjic-943	128	32	step	step	NOUN
hjic-943	128	33	by	by	ADP
hjic-943	128	34	numerical	numerical	ADJ
hjic-943	128	35	integration	integration	NOUN
hjic-943	128	36	.	.	PUNCT
hjic-943	129	1	in	in	ADP
hjic-943	129	2	order	order	NOUN
hjic-943	129	3	to	to	PART
hjic-943	129	4	distinguish	distinguish	VERB
hjic-943	129	5	the	the	DET
hjic-943	129	6	label	label	NOUN
hjic-943	129	7	<	<	X
hjic-943	129	8	s	s	X
hjic-943	129	9	>	>	X
hjic-943	129	10	assigned	assign	VERB
hjic-943	129	11	to	to	PART
hjic-943	129	12	differential	differential	VERB
hjic-943	129	13	variables	variable	NOUN
hjic-943	129	14	from	from	ADP
hjic-943	129	15	the	the	DET
hjic-943	129	16	label	label	NOUN
hjic-943	129	17	<	<	X
hjic-943	129	18	s	s	X
hjic-943	129	19	>	>	X
hjic-943	129	20	of	of	ADP
hjic-943	129	21	other	other	ADJ
hjic-943	129	22	variables	variable	NOUN
hjic-943	129	23	with	with	ADP
hjic-943	129	24	specified	specify	VERB
hjic-943	129	25	given	give	VERB
hjic-943	129	26	values	value	NOUN
hjic-943	129	27	the	the	DET
hjic-943	129	28	label	label	NOUN
hjic-943	129	29	of	of	ADP
hjic-943	129	30	differential	differential	ADJ
hjic-943	129	31	variables	variable	NOUN
hjic-943	129	32	is	be	AUX
hjic-943	129	33	denoted	denote	VERB
hjic-943	129	34	by	by	ADP
hjic-943	129	35	<	<	X
hjic-943	129	36	s	s	PROPN
hjic-943	129	37	*	*	NOUN
hjic-943	129	38	'	'	PUNCT
hjic-943	129	39	>	>	PUNCT
hjic-943	129	40	.	.	PUNCT
hjic-943	130	1	labels	label	VERB
hjic-943	130	2	<	<	X
hjic-943	130	3	s	s	X
hjic-943	130	4	>	>	X
hjic-943	130	5	and	and	CCONJ
hjic-943	130	6	<	<	X
hjic-943	130	7	s•	s•	NOUN
hjic-943	130	8	>	>	X
hjic-943	130	9	are	be	AUX
hjic-943	130	10	treated	treat	VERB
hjic-943	130	11	the	the	DET
hjic-943	130	12	same	same	ADJ
hjic-943	130	13	way	way	NOUN
hjic-943	130	14	in	in	ADP
hjic-943	130	15	the	the	DET
hjic-943	130	16	rest	rest	NOUN
hjic-943	130	17	of	of	ADP
hjic-943	130	18	this	this	DET
hjic-943	130	19	paper	paper	NOUN
hjic-943	130	20	.	.	PUNCT
hjic-943	131	1	•	•	NUM
hjic-943	131	2	<	<	X
hjic-943	131	3	g	g	X
hjic-943	131	4	>	>	X
hjic-943	131	5	(	(	PUNCT
hjic-943	131	6	gi\·en)-type	gi\·en)-type	NOUN
hjic-943	131	7	l'ariables	l'ariable	VERB
hjic-943	131	8	a	a	DET
hjic-943	131	9	variable	variable	NOUN
hjic-943	131	10	assigneq	assigneq	ADJ
hjic-943	131	11	to	to	ADP
hjic-943	131	12	a	a	DET
hjic-943	131	13	specific	specific	ADJ
hjic-943	131	14	value	value	NOUN
hjic-943	131	15	of	of	ADP
hjic-943	131	16	a	a	DET
hjic-943	131	17	left	left	ADJ
hjic-943	131	18	hand	hand	NOUN
hjic-943	131	19	side	side	NOUN
hjic-943	131	20	is	be	AUX
hjic-943	131	21	a	a	DET
hjic-943	131	22	<	<	X
hjic-943	131	23	g	g	PROPN
hjic-943	131	24	>	>	NOUN
hjic-943	131	25	·	·	PROPN
hjic-943	131	26	type	type	NOUN
hjic-943	131	27	variable	variable	NOUN
hjic-943	131	28	.	.	PUNCT
hjic-943	132	1	unlike	unlike	ADP
hjic-943	132	2	in	in	ADP
hjic-943	132	3	case	case	NOUN
hjic-943	132	4	of	of	ADP
hjic-943	132	5	<	<	X
hjic-943	132	6	s	s	X
hjic-943	132	7	>	>	X
hjic-943	132	8	-type	-type	NOUN
hjic-943	132	9	variables	variable	NOUN
hjic-943	132	10	the	the	DET
hjic-943	132	11	values	value	NOUN
hjic-943	132	12	of	of	ADP
hjic-943	132	13	the	the	DET
hjic-943	132	14	right	right	ADJ
hjic-943	132	15	band	band	NOUN
hjic-943	132	16	side	side	NOUN
hjic-943	132	17	variables	variable	NOUN
hjic-943	132	18	wm	wm	AUX
hjic-943	132	19	be	be	AUX
hjic-943	132	20	suitably	suitably	ADV
hjic-943	132	21	adjusted	adjust	VERB
hjic-943	132	22	so	so	SCONJ
hjic-943	132	23	as	as	SCONJ
hjic-943	132	24	to	to	PART
hjic-943	132	25	preserve	preserve	VERB
hjic-943	132	26	the	the	DET
hjic-943	132	27	equality	equality	NOUN
hjic-943	132	28	of	of	ADP
hjic-943	132	29	the	the	DET
hjic-943	132	30	two	two	NUM
hjic-943	132	31	sides	side	NOUN
hjic-943	132	32	.	.	PUNCT
hjic-943	133	1	the	the	DET
hjic-943	133	2	type	type	NOUN
hjic-943	133	3	<	<	X
hjic-943	133	4	g	g	X
hjic-943	133	5	>	>	X
hjic-943	133	6	is	be	AUX
hjic-943	133	7	usually	usually	ADV
hjic-943	133	8	assigned	assign	VERB
hjic-943	133	9	to	to	ADP
hjic-943	133	10	terminal	terminal	ADJ
hjic-943	133	11	vertices	vertex	NOUN
hjic-943	133	12	of	of	ADP
hjic-943	133	13	representation	representation	NOUN
hjic-943	133	14	graph	graph	NOUN
hjic-943	133	15	.	.	PUNCT
hjic-943	134	1	a	a	DET
hjic-943	134	2	non	non	ADJ
hjic-943	134	3	~	~	NOUN
hjic-943	134	4	terminal	terminal	ADJ
hjic-943	134	5	vertex	vertex	NOUN
hjic-943	134	6	assigned	assign	VERB
hjic-943	134	7	to	to	PART
hjic-943	134	8	type	type	VERB
hjic-943	134	9	<	<	X
hjic-943	134	10	g	g	X
hjic-943	134	11	>	>	X
hjic-943	134	12	can	can	AUX
hjic-943	134	13	be	be	AUX
hjic-943	134	14	split	split	VERB
hjic-943	134	15	into	into	ADP
hjic-943	134	16	two	two	NUM
hjic-943	134	17	copies	copy	NOUN
hjic-943	134	18	one	one	NUM
hjic-943	134	19	of	of	ADP
hjic-943	134	20	which	which	PRON
hjic-943	134	21	being	be	AUX
hjic-943	134	22	initial	initial	ADJ
hjic-943	134	23	and	and	CCONJ
hjic-943	134	24	the	the	DET
hjic-943	134	25	other	other	ADJ
hjic-943	134	26	which	which	PRON
hjic-943	134	27	being	be	AUX
hjic-943	134	28	terminal	terminal	ADJ
hjic-943	134	29	vertices	vertex	NOUN
hjic-943	134	30	.	.	PUNCT
hjic-943	135	1	the	the	DET
hjic-943	135	2	initial	initial	ADJ
hjic-943	135	3	vertex	vertex	NOUN
hjic-943	135	4	is	be	AUX
hjic-943	135	5	labeled	label	VERB
hjic-943	135	6	as	as	ADP
hjic-943	135	7	type	type	NOUN
hjic-943	135	8	<	<	X
hjic-943	135	9	s	s	X
hjic-943	135	10	>	>	X
hjic-943	135	11	and	and	CCONJ
hjic-943	135	12	the	the	DET
hjic-943	135	13	terminal	terminal	NOUN
hjic-943	135	14	as	as	ADP
hjic-943	135	15	type	type	NOUN
hjic-943	135	16	<	<	X
hjic-943	135	17	g	g	PROPN
hjic-943	135	18	>	>	X
hjic-943	135	19	.	.	PUNCT
hjic-943	136	1	as	as	ADP
hjic-943	136	2	a	a	DET
hjic-943	136	3	result	result	NOUN
hjic-943	136	4	,	,	PUNCT
hjic-943	136	5	vertices	vertex	NOUN
hjic-943	136	6	of	of	ADP
hjic-943	136	7	type	type	NOUN
hjic-943	136	8	<	<	X
hjic-943	136	9	g	g	X
hjic-943	136	10	>	>	X
hjic-943	136	11	form	form	NOUN
hjic-943	136	12	a	a	DET
hjic-943	136	13	subset	subset	NOUN
hjic-943	136	14	of	of	ADP
hjic-943	136	15	the	the	DET
hjic-943	136	16	terminal	terminal	ADJ
hjic-943	136	17	vertices	vertex	NOUN
hjic-943	136	18	.	.	PUNCT
hjic-943	137	1	according	accord	VERB
hjic-943	137	2	to	to	ADP
hjic-943	137	3	the	the	DET
hjic-943	137	4	representation	representation	NOUN
hjic-943	137	5	graph	graph	VERB
hjic-943	137	6	the	the	DET
hjic-943	137	7	value	value	NOUN
hjic-943	137	8	of	of	ADP
hjic-943	137	9	ev_ery	ev_ery	ADJ
hjic-943	137	10	variable	variable	NOUN
hjic-943	137	11	which	which	PRON
hjic-943	137	12	has	have	VERB
hjic-943	137	13	incoming	incoming	ADJ
hjic-943	137	14	arcs	arc	NOUN
hjic-943	137	15	only	only	ADV
hjic-943	137	16	from	from	ADP
hjic-943	137	17	vertices	vertex	NOUN
hjic-943	137	18	labeled	label	VERB
hjic-943	137	19	by	by	ADP
hjic-943	137	20	type	type	NOUN
hjic-943	137	21	<	<	X
hjic-943	137	22	s	s	X
hjic-943	137	23	>	>	X
hjic-943	137	24	can	can	AUX
hjic-943	137	25	be	be	AUX
hjic-943	137	26	calculated	calculate	VERB
hjic-943	137	27	by	by	ADP
hjic-943	137	28	simple	simple	ADJ
hjic-943	137	29	substitution	substitution	NOUN
hjic-943	137	30	in	in	ADP
hjic-943	137	31	~	~	X
hjic-943	137	32	o	o	X
hjic-943	137	33	the	the	DET
hjic-943	137	34	corresponding	correspond	VERB
hjic-943	137	35	equation	equation	NOUN
hjic-943	137	36	.	.	PUNCT
hjic-943	138	1	these	these	DET
hjic-943	138	2	variables	variable	NOUN
hjic-943	138	3	become	become	AUX
hjic-943	138	4	secondarily	secondarily	ADV
hjic-943	138	5	labeled	label	VERB
hjic-943	138	6	by	by	ADP
hjic-943	138	7	type	type	NOUN
hjic-943	138	8	<	<	X
hjic-943	138	9	s	s	X
hjic-943	138	10	>	>	X
hjic-943	138	11	.	.	PUNCT
hjic-943	139	1	after	after	ADP
hjic-943	139	2	this	this	PRON
hjic-943	139	3	we	we	PRON
hjic-943	139	4	can	can	AUX
hjic-943	139	5	calculate	calculate	VERB
hjic-943	139	6	the	the	DET
hjic-943	139	7	value	value	NOUN
hjic-943	139	8	of	of	ADP
hjic-943	139	9	all	all	DET
hjic-943	139	10	variables	variable	NOUN
hjic-943	139	11	which	which	PRON
hjic-943	139	12	have	have	VERB
hjic-943	139	13	incoming	incoming	ADJ
hjic-943	139	14	arcs	arc	NOUN
hjic-943	139	15	only	only	ADV
hjic-943	139	16	from	from	ADP
hjic-943	139	17	vertices	vertex	NOUN
hjic-943	139	18	primarily	primarily	ADV
hjic-943	139	19	and	and	CCONJ
hjic-943	139	20	secondarily	secondarily	ADV
hjic-943	139	21	labeled	label	VERB
hjic-943	139	22	by	by	ADP
hjic-943	139	23	type	type	NOUN
hjic-943	139	24	<	<	X
hjic-943	139	25	s	s	X
hjic-943	139	26	>	>	X
hjic-943	139	27	by	by	ADP
hjic-943	139	28	simple	simple	ADJ
hjic-943	139	29	substitution	substitution	NOUN
hjic-943	139	30	.	.	PUNCT
hjic-943	140	1	these	these	DET
hjic-943	140	2	variables	variable	NOUN
hjic-943	140	3	will	will	AUX
hjic-943	140	4	be	be	AUX
hjic-943	140	5	tertiarily	tertiarily	ADV
hjic-943	140	6	labeled	label	VERB
hjic-943	140	7	by	by	ADP
hjic-943	140	8	type	type	NOUN
hjic-943	140	9	<	<	X
hjic-943	140	10	s	s	X
hjic-943	140	11	>	>	X
hjic-943	140	12	and	and	CCONJ
hjic-943	140	13	this	this	DET
hjic-943	140	14	process	process	NOUN
hjic-943	140	15	can	can	AUX
hjic-943	140	16	be	be	AUX
hjic-943	140	17	repeat	repeat	VERB
hjic-943	140	18	~	~	ADP
hjic-943	141	1	d	d	NOUN
hjic-943	141	2	if	if	SCONJ
hjic-943	141	3	necess	necess	NOUN
hjic-943	141	4	~	~	PUNCT
hjic-943	141	5	y.	y.	NOUN
hjic-943	141	6	omitting	omit	VERB
hjic-943	141	7	all	all	DET
hjic-943	141	8	vertices	vertex	NOUN
hjic-943	141	9	labeled	label	VERB
hjic-943	141	10	primarily	primarily	ADV
hjic-943	141	11	,	,	PUNCT
hjic-943	141	12	secondanly	secondanly	ADV
hjic-943	141	13	,	,	PUNCT
hjic-943	141	14	_	_	PRON
hjic-943	141	15	etc	etc	X
hjic-943	141	16	.	.	X
hjic-943	141	17	by	by	ADP
hjic-943	141	18	type	type	NOUN
hjic-943	141	19	<	<	X
hjic-943	141	20	s	s	X
hjic-943	141	21	>	>	X
hjic-943	141	22	and	and	CCONJ
hjic-943	141	23	all	all	DET
hjic-943	141	24	arcs	arc	NOUN
hjic-943	141	25	starting	start	VERB
hjic-943	141	26	from	from	ADP
hjic-943	141	27	them	they	PRON
hjic-943	141	28	from	from	ADP
hjic-943	141	29	the	the	DET
hjic-943	141	30	representation	representation	NOUN
hjic-943	141	31	graph	graph	NOUN
hjic-943	141	32	we	we	PRON
hjic-943	141	33	obtain	obtain	VERB
hjic-943	141	34	the	the	DET
hjic-943	141	35	reduced	reduced	ADJ
hjic-943	141	36	gr	gr	NOUN
hjic-943	141	37	~	~	NOUN
hjic-943	141	38	ph	ph	VERB
hjic-943	141	39	.	.	PUNCT
hjic-943	142	1	the	the	DET
hjic-943	142	2	classification	classification	NOUN
hjic-943	142	3	of	of	ADP
hjic-943	142	4	vertices	vertex	NOUN
hjic-943	142	5	of	of	ADP
hjic-943	142	6	a	a	DET
hjic-943	142	7	reduced	reduce	VERB
hjic-943	142	8	graph	graph	NOUN
hjic-943	142	9	1s	1	NOUN
hjic-943	142	10	as	as	SCONJ
hjic-943	142	11	follows	follow	VERB
hjic-943	142	12	:	:	PUNCT
hjic-943	142	13	•	•	NOUN
hjic-943	142	14	all	all	DET
hjic-943	142	15	initial	initial	ADJ
hjic-943	142	16	vertices	vertex	NOUN
hjic-943	142	17	form	form	VERB
hjic-943	142	18	the	the	DET
hjic-943	142	19	unknown	unknown	ADJ
hjic-943	142	20	variable	variable	NOUN
hjic-943	142	21	set	set	NOUN
hjic-943	142	22	x	x	SYM
hjic-943	142	23	,	,	PUNCT
hjic-943	142	24	•	•	PRON
hjic-943	142	25	all	all	DET
hjic-943	142	26	terminal	terminal	ADJ
hjic-943	142	27	vertices	vertex	NOUN
hjic-943	142	28	labeled	label	VERB
hjic-943	142	29	by	by	ADP
hjic-943	142	30	type	type	NOUN
hjic-943	142	31	<	<	X
hjic-943	142	32	g	g	X
hjic-943	142	33	>	>	X
hjic-943	142	34	constitute	constitute	VERB
hjic-943	142	35	the	the	DET
hjic-943	142	36	known	know	VERB
hjic-943	142	37	variable	variable	NOUN
hjic-943	142	38	(	(	PUNCT
hjic-943	142	39	parameter	parameter	NOUN
hjic-943	142	40	)	)	PUNCT
hjic-943	142	41	set	set	VERB
hjic-943	142	42	y	y	PROPN
hjic-943	142	43	,	,	PUNCT
hjic-943	142	44	•	•	VERB
hjic-943	142	45	all	all	DET
hjic-943	142	46	other	other	ADJ
hjic-943	142	47	vertices	vertex	NOUN
hjic-943	142	48	constitute	constitute	VERB
hjic-943	142	49	the	the	DET
hjic-943	142	50	unknown	unknown	ADJ
hjic-943	142	51	variable	variable	NOUN
hjic-943	142	52	set	set	VERB
hjic-943	142	53	u.	u.	PROPN
hjic-943	142	54	differential	differential	PROPN
hjic-943	142	55	algebraic	algebraic	ADJ
hjic-943	142	56	equations	equation	NOUN
hjic-943	142	57	and	and	CCONJ
hjic-943	142	58	the	the	DET
hjic-943	142	59	differential	differential	ADJ
hjic-943	142	60	index	index	NOUN
hjic-943	142	61	the	the	DET
hjic-943	142	62	degree	degree	NOUN
hjic-943	142	63	of	of	ADP
hjic-943	142	64	difficulty	difficulty	NOUN
hjic-943	142	65	to	to	PART
hjic-943	142	66	solve	solve	VERB
hjic-943	142	67	a	a	DET
hjic-943	142	68	dab	dab	NOUN
hjic-943	142	69	-	-	PUNCT
hjic-943	142	70	system	system	NOUN
hjic-943	142	71	f(z(t	f(z(t	NOUN
hjic-943	142	72	)	)	PUNCT
hjic-943	142	73	,	,	PUNCT
hjic-943	142	74	z'(t	z'(t	NOUN
hjic-943	142	75	)	)	PUNCT
hjic-943	142	76	,	,	PUNCT
hjic-943	142	77	t	t	PROPN
hjic-943	142	78	)	)	PUNCT
hjic-943	143	1	=	=	SYM
hjic-943	143	2	0	0	PUNCT
hjic-943	143	3	can	can	AUX
hjic-943	143	4	be	be	AUX
hjic-943	143	5	characterized	characterize	VERB
hjic-943	143	6	by	by	ADP
hjic-943	143	7	the	the	DET
hjic-943	143	8	differential	differential	ADJ
hjic-943	143	9	index	index	NOUN
hjic-943	143	10	of	of	ADP
hjic-943	143	11	the	the	DET
hjic-943	143	12	model	model	NOUN
hjic-943	143	13	.	.	PUNCT
hjic-943	144	1	the	the	DET
hjic-943	144	2	definition	definition	NOUN
hjic-943	144	3	of	of	ADP
hjic-943	144	4	the	the	DET
hjic-943	144	5	differential	differential	ADJ
hjic-943	144	6	index	index	NOUN
hjic-943	144	7	[	[	X
hjic-943	144	8	1	1	NUM
hjic-943	144	9	]	]	PUNCT
hjic-943	144	10	is	be	AUX
hjic-943	144	11	as	as	SCONJ
hjic-943	144	12	follows	follow	VERB
hjic-943	144	13	.	.	PUNCT
hjic-943	145	1	the	the	DET
hjic-943	145	2	minimum	minimum	ADJ
hjic-943	145	3	number	number	NOUN
hjic-943	145	4	of	of	ADP
hjic-943	145	5	times	time	NOUN
hjic-943	145	6	that	that	PRON
hjic-943	145	7	all	all	PRON
hjic-943	145	8	or	or	CCONJ
hjic-943	145	9	part	part	NOUN
hjic-943	145	10	of	of	ADP
hjic-943	145	11	a	a	DET
hjic-943	145	12	dab	dab	NOUN
hjic-943	145	13	-	-	PUNCT
hjic-943	145	14	system	system	NOUN
hjic-943	145	15	f(z(t	f(z(t	NOUN
hjic-943	145	16	)	)	PUNCT
hjic-943	145	17	,	,	PUNCT
hjic-943	145	18	z'(t	z'(t	NOUN
hjic-943	145	19	)	)	PUNCT
hjic-943	145	20	,	,	PUNCT
hjic-943	145	21	t	t	PROPN
hjic-943	145	22	)	)	PUNCT
hjic-943	145	23	=	=	SYM
hjic-943	145	24	0	0	PUNCT
hjic-943	145	25	must	must	AUX
hjic-943	145	26	be	be	AUX
hjic-943	145	27	differentiated	differentiate	VERB
hjic-943	145	28	with	with	ADP
hjic-943	145	29	respect	respect	NOUN
hjic-943	145	30	to	to	ADP
hjic-943	145	31	time	time	NOUN
hjic-943	145	32	in	in	ADP
hjic-943	145	33	order	order	NOUN
hjic-943	145	34	to	to	PART
hjic-943	145	35	determine	determine	VERB
hjic-943	145	36	z	z	NOUN
hjic-943	145	37	'	'	PUNCT
hjic-943	145	38	as	as	ADP
hjic-943	145	39	a	a	DET
hjic-943	145	40	continuous	continuous	ADJ
hjic-943	145	41	function	function	NOUN
hjic-943	145	42	of	of	ADP
hjic-943	145	43	z	z	PROPN
hjic-943	145	44	and	and	CCONJ
hjic-943	145	45	t	t	PROPN
hjic-943	145	46	is	be	AUX
hjic-943	145	47	the	the	DET
hjic-943	145	48	differential	differential	ADJ
hjic-943	145	49	index	index	NOUN
hjic-943	145	50	of	of	ADP
hjic-943	145	51	the	the	DET
hjic-943	145	52	dae	dae	NOUN
hjic-943	145	53	-	-	PUNCT
hjic-943	145	54	system	system	NOUN
hjic-943	145	55	.	.	PUNCT
hjic-943	146	1	numerical	numerical	ADJ
hjic-943	146	2	solution	solution	NOUN
hjic-943	146	3	of	of	ADP
hjic-943	146	4	daes	daes	PROPN
hjic-943	146	5	includes	include	VERB
hjic-943	146	6	both	both	DET
hjic-943	146	7	initialization	initialization	NOUN
hjic-943	146	8	and	and	CCONJ
hjic-943	146	9	integration	integration	NOUN
hjic-943	146	10	.	.	PUNCT
hjic-943	147	1	to	to	PART
hjic-943	147	2	·	·	PUNCT
hjic-943	147	3	solve	solve	VERB
hjic-943	147	4	daes	daes	PROPN
hjic-943	147	5	successfully	successfully	ADV
hjic-943	147	6	the	the	DET
hjic-943	147	7	initial	initial	ADJ
hjic-943	147	8	values	value	NOUN
hjic-943	147	9	must	must	AUX
hjic-943	147	10	be	be	AUX
hjic-943	147	11	consistent	consistent	ADJ
hjic-943	147	12	.	.	PUNCT
hjic-943	148	1	in	in	ADP
hjic-943	148	2	case	case	NOUN
hjic-943	148	3	of	of	ADP
hjic-943	148	4	odes	ode	VERB
hjic-943	148	5	the	the	DET
hjic-943	148	6	initial	initial	ADJ
hjic-943	148	7	values	value	NOUN
hjic-943	148	8	can	can	AUX
hjic-943	148	9	be	be	AUX
hjic-943	148	10	chosen	choose	VERB
hjic-943	148	11	independently	independently	ADV
hjic-943	148	12	hence	hence	ADV
hjic-943	148	13	the	the	DET
hjic-943	148	14	so	so	ADV
hjic-943	148	15	called	call	VERB
hjic-943	148	16	dynamic	dynamic	ADJ
hjic-943	148	17	degree	degree	NOUN
hjic-943	148	18	of	of	ADP
hjic-943	148	19	freedom	freedom	NOUN
hjic-943	148	20	is	be	AUX
hjic-943	148	21	equal	equal	ADJ
hjic-943	148	22	to	to	ADP
hjic-943	148	23	the	the	DET
hjic-943	148	24	number	number	NOUN
hjic-943	148	25	of	of	ADP
hjic-943	148	26	differential	differential	ADJ
hjic-943	148	27	equations	equation	NOUN
hjic-943	148	28	.	.	PUNCT
hjic-943	149	1	in	in	ADP
hjic-943	149	2	contrast	contrast	NOUN
hjic-943	149	3	to	to	ADP
hjic-943	149	4	this	this	PRON
hjic-943	149	5	the	the	DET
hjic-943	149	6	initial	initial	ADJ
hjic-943	149	7	values	value	NOUN
hjic-943	149	8	of	of	ADP
hjic-943	149	9	daes	daes	PROPN
hjic-943	149	10	can	can	AUX
hjic-943	149	11	be	be	AUX
hjic-943	149	12	constrained	constrain	VERB
hjic-943	149	13	by	by	ADP
hjic-943	149	14	the	the	DET
hjic-943	149	15	algebraic	algebraic	ADJ
hjic-943	149	16	equations	equation	NOUN
hjic-943	149	17	,	,	PUNCT
hjic-943	149	18	so	so	SCONJ
hjic-943	149	19	the	the	DET
hjic-943	149	20	initialization	initialization	NOUN
hjic-943	149	21	of	of	ADP
hjic-943	149	22	daes	daes	PROPN
hjic-943	149	23	can	can	AUX
hjic-943	149	24	be	be	AUX
hjic-943	149	25	cumbersome	cumbersome	ADJ
hjic-943	149	26	and	and	CCONJ
hjic-943	149	27	the	the	DET
hjic-943	149	28	problems	problem	NOUN
hjic-943	149	29	related	relate	VERB
hjic-943	149	30	to	to	ADP
hjic-943	149	31	initialization	initialization	NOUN
hjic-943	149	32	increase	increase	NOUN
hjic-943	149	33	with	with	ADP
hjic-943	149	34	higher	high	ADJ
hjic-943	149	35	index	index	NOUN
hjic-943	149	36	values	value	NOUN
hjic-943	149	37	.	.	PUNCT
hjic-943	150	1	difficulty	difficulty	NOUN
hjic-943	150	2	of	of	ADP
hjic-943	150	3	numerical	numerical	ADJ
hjic-943	150	4	integration	integration	NOUN
hjic-943	150	5	of	of	ADP
hjic-943	150	6	daes	daes	PROPN
hjic-943	150	7	also	also	ADV
hjic-943	150	8	increases	increase	VERB
hjic-943	150	9	with	with	ADP
hjic-943	150	10	higher	high	ADJ
hjic-943	150	11	index	index	NOUN
hjic-943	150	12	values	value	NOUN
hjic-943	150	13	[	[	X
hjic-943	150	14	3	3	NUM
hjic-943	150	15	]	]	PUNCT
hjic-943	150	16	.	.	PUNCT
hjic-943	151	1	dynamic	dynamic	ADJ
hjic-943	151	2	process	process	NOUN
hjic-943	151	3	models	model	NOUN
hjic-943	151	4	can	can	AUX
hjic-943	151	5	be	be	AUX
hjic-943	151	6	described	describe	VERB
hjic-943	151	7	by	by	ADP
hjic-943	151	8	semi­	semi­	NOUN
hjic-943	151	9	explicit	explicit	ADJ
hjic-943	151	10	daes	daes	PROPN
hjic-943	151	11	as	as	SCONJ
hjic-943	151	12	follows	follow	VERB
hjic-943	151	13	[	[	X
hjic-943	151	14	4	4	NUM
hjic-943	151	15	]	]	X
hjic-943	151	16	:	:	PUNCT
hjic-943	152	1	z	z	X
hjic-943	152	2	;	;	PUNCT
hjic-943	152	3	=	=	SYM
hjic-943	152	4	f(z1	f(z1	NOUN
hjic-943	152	5	~z2	~z2	PUNCT
hjic-943	152	6	,	,	PUNCT
hjic-943	152	7	t	t	PROPN
hjic-943	152	8	)	)	PUNCT
hjic-943	152	9	,	,	PUNCT
hjic-943	152	10	z1(t0	z1(t0	NOUN
hjic-943	152	11	)	)	PUNCT
hjic-943	153	1	=	=	SYM
hjic-943	153	2	=	=	SYM
hjic-943	153	3	zlo	zlo	PROPN
hjic-943	153	4	(	(	PUNCT
hjic-943	153	5	17	17	NUM
hjic-943	153	6	)	)	PUNCT
hjic-943	153	7	0	0	NUM
hjic-943	154	1	=	=	NUM
hjic-943	154	2	g(zpz2	g(zpz2	NOUN
hjic-943	154	3	,	,	PUNCT
hjic-943	154	4	t	t	PROPN
hjic-943	154	5	)	)	PUNCT
hjic-943	154	6	(	(	PUNCT
hjic-943	154	7	18	18	NUM
hjic-943	154	8	)	)	PUNCT
hjic-943	154	9	according	accord	VERB
hjic-943	154	10	to	to	ADP
hjic-943	154	11	the	the	DET
hjic-943	154	12	definition	definition	NOUN
hjic-943	154	13	of	of	ADP
hjic-943	154	14	the	the	DET
hjic-943	154	15	differential	differential	ADJ
hjic-943	154	16	index	index	NOUN
hjic-943	154	17	a	a	DET
hjic-943	154	18	semi	semi	ADJ
hjic-943	154	19	~	~	NOUN
hjic-943	154	20	explicit	explicit	ADJ
hjic-943	154	21	dae	dae	NOUN
hjic-943	154	22	has	have	VERB
hjic-943	154	23	index	index	NOUN
hjic-943	154	24	one	one	NOUN
hjic-943	154	25	if	if	SCONJ
hjic-943	154	26	and	and	CCONJ
hjic-943	154	27	only	only	ADV
hjic-943	154	28	if	if	SCONJ
hjic-943	154	29	one	one	NUM
hjic-943	154	30	differentiation	differentiation	NOUN
hjic-943	154	31	is	be	AUX
hjic-943	154	32	sufficient	sufficient	ADJ
hjic-943	154	33	to	to	PART
hjic-943	154	34	express	express	VERB
hjic-943	154	35	z'2	z'2	NOUN
hjic-943	154	36	as	as	ADP
hjic-943	154	37	a	a	DET
hjic-943	154	38	continuous	continuous	ADJ
hjic-943	154	39	function	function	NOUN
hjic-943	154	40	of	of	ADP
hjic-943	154	41	z	z	PROPN
hjic-943	154	42	~	~	PROPN
hjic-943	154	43	o	o	PROPN
hjic-943	154	44	z2	z2	NOUN
hjic-943	154	45	and	and	CCONJ
hjic-943	154	46	t.	t.	NOUN
hjic-943	154	47	one	one	NUM
hjic-943	154	48	differentiation	differentiation	NOUN
hjic-943	154	49	is	be	AUX
hjic-943	154	50	sufficient	sufficient	ADJ
hjic-943	154	51	only	only	ADV
hjic-943	154	52	if	if	SCONJ
hjic-943	154	53	the	the	DET
hjic-943	154	54	jacobian	jacobian	ADJ
hjic-943	154	55	matrix	matrix	NOUN
hjic-943	154	56	gz2	gz2	NOUN
hjic-943	154	57	is	be	AUX
hjic-943	154	58	non	non	ADJ
hjic-943	154	59	-	-	ADJ
hjic-943	154	60	singular	singular	ADJ
hjic-943	154	61	.	.	PUNCT
hjic-943	155	1	p	p	PROPN
hjic-943	155	2	fig.3	fig.3	PROPN
hjic-943	155	3	a	a	DET
hjic-943	155	4	simple	simple	ADJ
hjic-943	155	5	liquid	liquid	ADJ
hjic-943	155	6	system	system	NOUN
hjic-943	155	7	structural	structural	ADJ
hjic-943	155	8	non	non	ADJ
hjic-943	155	9	-	-	NOUN
hjic-943	155	10	singularity	singularity	NOUN
hjic-943	155	11	of	of	ADP
hjic-943	155	12	gz2	gz2	NOUN
hjic-943	155	13	i.e.	i.e.	X
hjic-943	155	14	the	the	DET
hjic-943	155	15	full	full	ADJ
hjic-943	155	16	structural	structural	ADJ
hjic-943	155	17	rank	rank	NOUN
hjic-943	155	18	of	of	ADP
hjic-943	155	19	gz2	gz2	PROPN
hjic-943	155	20	results	result	NOUN
hjic-943	155	21	in	in	ADP
hjic-943	155	22	a	a	DET
hjic-943	155	23	model	model	NOUN
hjic-943	155	24	which	which	PRON
hjic-943	155	25	is	be	AUX
hjic-943	155	26	structurally	structurally	ADV
hjic-943	155	27	semi­	semi­	ADJ
hjic-943	155	28	explicit	explicit	ADJ
hjic-943	155	29	index	index	NOUN
hjic-943	155	30	1	1	NUM
hjic-943	155	31	.	.	PUNCT
hjic-943	156	1	the	the	DET
hjic-943	156	2	initial	initial	ADJ
hjic-943	156	3	values	value	NOUN
hjic-943	156	4	of	of	ADP
hjic-943	156	5	the	the	DET
hjic-943	156	6	differential	differential	ADJ
hjic-943	156	7	variables	variable	NOUN
hjic-943	156	8	in	in	ADP
hjic-943	156	9	the	the	DET
hjic-943	156	10	semi	semi	ADJ
hjic-943	156	11	-	-	ADJ
hjic-943	156	12	explicit	explicit	ADJ
hjic-943	156	13	index	index	NOUN
hjic-943	156	14	one	one	NUM
hjic-943	156	15	models	model	NOUN
hjic-943	156	16	may	may	AUX
hjic-943	156	17	be	be	AUX
hjic-943	156	18	chosen	choose	VERB
hjic-943	156	19	independently	independently	ADV
hjic-943	156	20	.	.	PUNCT
hjic-943	156	21	.	.	PUNCT
hjic-943	157	1	if	if	SCONJ
hjic-943	157	2	gz2	gz2	PROPN
hjic-943	157	3	is	be	AUX
hjic-943	157	4	singular	singular	ADJ
hjic-943	157	5	then	then	ADV
hjic-943	157	6	the	the	DET
hjic-943	157	7	differential	differential	ADJ
hjic-943	157	8	index	index	NOUN
hjic-943	157	9	is	be	AUX
hjic-943	157	10	greater	great	ADJ
hjic-943	157	11	than	than	ADP
hjic-943	157	12	1	1	NUM
hjic-943	157	13	.	.	PUNCT
hjic-943	157	14	structural	structural	ADJ
hjic-943	157	15	singularity	singularity	NOUN
hjic-943	157	16	of	of	ADP
hjic-943	157	17	gz2	gz2	NOUN
hjic-943	157	18	is	be	AUX
hjic-943	157	19	a	a	DET
hjic-943	157	20	sufficient	sufficient	ADJ
hjic-943	157	21	conditio~	conditio~	PROPN
hjic-943	157	22	for	for	ADP
hjic-943	157	23	differential	differential	ADJ
hjic-943	157	24	index	index	NOUN
hjic-943	157	25	being	be	AUX
hjic-943	157	26	>	>	X
hjic-943	157	27	1	1	NUM
hjic-943	157	28	numerically	numerically	ADV
hjic-943	157	29	.	.	PUNCT
hjic-943	158	1	i~	i~	ADJ
hjic-943	158	2	pract	pract	NOUN
hjic-943	158	3	:	:	PUNCT
hjic-943	158	4	ce	ce	PROPN
hjic-943	158	5	.	.	PUNCT
hjic-943	159	1	most	most	ADJ
hjic-943	159	2	of	of	ADP
hjic-943	159	3	dynamic	dynamic	ADJ
hjic-943	159	4	process	process	NOUN
hjic-943	159	5	models	model	NOUN
hjic-943	159	6	having	have	VERB
hjic-943	159	7	differential	differential	ADJ
hjic-943	159	8	mdex	mdex	NOUN
hjic-943	159	9	>	>	X
hjic-943	159	10	1	1	NUM
hjic-943	159	11	are	be	AUX
hjic-943	159	12	semi	semi	ADJ
hjic-943	159	13	-	-	ADJ
hjic-943	159	14	explicit	explicit	ADJ
hjic-943	159	15	index	index	NOUN
hjic-943	159	16	2	2	NUM
hjic-943	159	17	models	model	NOUN
hjic-943	159	18	,	,	PUNCT
hjic-943	159	19	?	?	PUNCT
hjic-943	160	1	ut	ut	PROPN
hjic-943	160	2	there	there	PRON
hjic-943	160	3	are	be	VERB
hjic-943	160	4	models	model	NOUN
hjic-943	160	5	having	have	VERB
hjic-943	160	6	arbitrarily	arbitrarily	ADV
hjic-943	160	7	large	large	ADJ
hjic-943	160	8	differential	differential	ADJ
hjic-943	160	9	mdex	mdex	NOUN
hjic-943	160	10	[	[	X
hjic-943	160	11	8	8	NUM
hjic-943	160	12	]	]	PUNCT
hjic-943	160	13	.	.	PUNCT
hjic-943	161	1	the	the	DET
hjic-943	161	2	initial	initial	ADJ
hjic-943	161	3	values	value	NOUN
hjic-943	161	4	of	of	ADP
hjic-943	161	5	the	the	DET
hjic-943	161	6	differential	differential	ADJ
hjic-943	161	7	variables	variable	NOUN
hjic-943	161	8	in	in	ADP
hjic-943	161	9	the	the	DET
hjic-943	161	10	higher	high	ADJ
hjic-943	161	11	index	index	NOUN
hjic-943	161	12	semi	semi	ADJ
hjic-943	161	13	-	-	ADJ
hjic-943	161	14	explicit	explicit	ADJ
hjic-943	161	15	models	model	NOUN
hjic-943	161	16	can	can	AUX
hjic-943	161	17	not	not	PART
hjic-943	161	18	be	be	AUX
hjic-943	161	19	chosen	choose	VERB
hjic-943	161	20	independently	independently	ADV
hjic-943	161	21	.	.	PUNCT
hjic-943	162	1	hi	hi	VERB
hjic-943	162	2	~	~	NOUN
hjic-943	162	3	h	h	NOUN
hjic-943	162	4	index	index	NOUN
hjic-943	162	5	models	model	NOUN
hjic-943	162	6	c.an	c.an	NOUN
hjic-943	162	7	either	either	CCONJ
hjic-943	162	8	be	be	AUX
hjic-943	162	9	simulated	simulate	VERB
hjic-943	162	10	directly	directly	ADV
hjic-943	162	11	by	by	ADP
hjic-943	162	12	an	an	DET
hjic-943	162	13	mtegrator	mtegrator	NOUN
hjic-943	162	14	which	which	PRON
hjic-943	162	15	tackles	tackle	VERB
hjic-943	162	16	high	high	ADJ
hjic-943	162	17	index	index	NOUN
hjic-943	162	18	daes	daes	PROPN
hjic-943	162	19	or	or	CCONJ
hjic-943	162	20	be	be	AUX
hjic-943	162	21	transformed	transform	VERB
hjic-943	162	22	to	to	ADP
hjic-943	162	23	semi	semi	ADJ
hjic-943	162	24	-	-	ADJ
hjic-943	162	25	explicit	explicit	ADJ
hjic-943	162	26	index	index	NOUN
hjic-943	162	27	1	1	NUM
hjic-943	162	28	model	model	NOUN
hjic-943	162	29	and	and	CCONJ
hjic-943	162	30	then	then	ADV
hjic-943	162	31	integrated	integrate	VERB
hjic-943	162	32	.	.	PUNCT
hjic-943	163	1	investigation	investigation	NOUN
hjic-943	163	2	of	of	ADP
hjic-943	163	3	structural	structural	ADJ
hjic-943	163	4	solvability	solvability	NOUN
hjic-943	163	5	of	of	ADP
hjic-943	163	6	dynamic	dynamic	ADJ
hjic-943	163	7	process	process	NOUN
hjic-943	163	8	models	model	NOUN
hjic-943	163	9	in	in	ADP
hjic-943	163	10	our	our	PRON
hjic-943	163	11	earlier	early	ADJ
hjic-943	163	12	work	work	NOUN
hjic-943	163	13	[	[	X
hjic-943	163	14	7	7	X
hjic-943	163	15	]	]	PUNCT
hjic-943	163	16	a	a	DET
hjic-943	163	17	graphical	graphical	ADJ
hjic-943	163	18	technique	technique	NOUN
hjic-943	163	19	is	be	AUX
hjic-943	163	20	p	p	X
hjic-943	163	21	:	:	PUNCT
hjic-943	163	22	esented	esented	ADJ
hjic-943	163	23	which	which	PRON
hjic-943	163	24	is	be	AUX
hjic-943	163	25	suitable	suitable	ADJ
hjic-943	163	26	to	to	PART
hjic-943	163	27	compute	compute	VERB
hjic-943	163	28	the	the	DET
hjic-943	163	29	structural	structural	ADJ
hjic-943	163	30	differential	differential	ADJ
hjic-943	163	31	index	index	NOUN
hjic-943	163	32	of	of	ADP
hjic-943	163	33	lumped	lump	VERB
hjic-943	163	34	dynamic	dynamic	ADJ
hjic-943	163	35	process	process	NOUN
hjic-943	163	36	models	model	NOUN
hjic-943	163	37	.	.	PUNCT
hjic-943	163	38	!	!	PUNCT
hjic-943	164	1	he	he	PRON
hjic-943	164	2	characteristic	characteristic	ADJ
hjic-943	164	3	features	feature	NOUN
hjic-943	164	4	of	of	ADP
hjic-943	164	5	the	the	DET
hjic-943	164	6	representation	representation	NOUN
hjic-943	164	7	graph	graph	NOUN
hjic-943	164	8	of	of	ADP
hjic-943	164	9	mdex	mdex	NOUN
hjic-943	164	10	1	1	NUM
hjic-943	164	11	and	and	CCONJ
hjic-943	164	12	high	high	ADJ
hjic-943	164	13	index	index	NOUN
hjic-943	164	14	semi	semi	ADJ
hjic-943	164	15	-	-	ADJ
hjic-943	164	16	explicit	explicit	ADJ
hjic-943	164	17	dab	dab	NOUN
hjic-943	164	18	-	-	PUNCT
hjic-943	164	19	models	model	NOUN
hjic-943	164	20	are	be	AUX
hjic-943	164	21	also	also	ADV
hjic-943	164	22	described	describe	VERB
hjic-943	164	23	there	there	ADV
hjic-943	164	24	.	.	PUNCT
hjic-943	164	25	.	.	PUNCT
hjic-943	165	1	based	base	VERB
hjic-943	165	2	on	on	ADP
hjic-943	165	3	the	the	DET
hjic-943	165	4	structural	structural	ADJ
hjic-943	165	5	solvability	solvability	NOUN
hjic-943	165	6	properties	property	NOUN
hjic-943	165	7	a	a	DET
hjic-943	165	8	novel	novel	ADJ
hjic-943	165	9	~ndex	~ndex	NOUN
hjic-943	165	10	reduction	reduction	NOUN
hjic-943	165	11	algorithm	algorithm	NOUN
hjic-943	165	12	has	have	AUX
hjic-943	165	13	been	be	AUX
hjic-943	165	14	proposed	propose	VERB
hjic-943	165	15	for	for	ADP
hjic-943	165	16	both	both	PRON
hjic-943	165	17	mde~	mde~	NUM
hjic-943	165	18	2	2	NUM
hjic-943	165	19	and	and	CCONJ
hjic-943	165	20	higher	high	ADJ
hjic-943	165	21	index	index	NOUN
hjic-943	165	22	models	model	NOUN
hjic-943	165	23	.	.	PUNCT
hjic-943	166	1	the	the	DET
hjic-943	166	2	developed	develop	VERB
hjic-943	166	3	algonthm	algonthm	NOUN
hjic-943	166	4	can	can	AUX
hjic-943	166	5	also	also	ADV
hjic-943	166	6	be	be	AUX
hjic-943	166	7	used	use	VERB
hjic-943	166	8	for	for	ADP
hjic-943	166	9	the	the	DET
hjic-943	166	10	investigation	investigation	NOUN
hjic-943	166	11	of	of	ADP
hjic-943	166	12	the	the	DET
hjic-943	166	13	structural	structural	ADJ
hjic-943	166	14	differential	differential	ADJ
hjic-943	166	15	index	index	NOUN
hjic-943	166	16	and	and	CCONJ
hjic-943	166	17	the	the	DET
hjic-943	166	18	structural	structural	ADJ
hjic-943	166	19	solvability	solvability	NOUN
hjic-943	166	20	of	of	ADP
hjic-943	166	21	these	these	DET
hjic-943	166	22	models	model	NOUN
hjic-943	166	23	.	.	PUNCT
hjic-943	167	1	these	these	DET
hjic-943	167	2	results	result	NOUN
hjic-943	167	3	are	be	AUX
hjic-943	167	4	illustrated	illustrate	VERB
hjic-943	167	5	on	on	ADP
hjic-943	167	6	the	the	DET
hjic-943	167	7	following	follow	VERB
hjic-943	167	8	example	example	NOUN
hjic-943	167	9	.	.	PUNCT
hjic-943	167	10	.	.	PUNCT
hjic-943	168	1	example	example	NOUN
hjic-943	169	1	2	2	NUM
hjic-943	169	2	.	.	X
hjic-943	169	3	consider	consider	VERB
hjic-943	169	4	a	a	DET
hjic-943	169	5	liquid	liquid	ADJ
hjic-943	169	6	tank	tank	NOUN
hjic-943	169	7	system	system	NOUN
hjic-943	169	8	with	with	ADP
hjic-943	169	9	one	one	NUM
hjic-943	169	10	mlet	mlet	NOUN
hjic-943	169	11	stream	stream	NOUN
hjic-943	169	12	and	and	CCONJ
hjic-943	169	13	one	one	NUM
hjic-943	169	14	exit	exit	NOUN
hjic-943	169	15	stream	stream	NOUN
hjic-943	169	16	as	as	SCONJ
hjic-943	169	17	is	be	AUX
hjic-943	169	18	shown	show	VERB
hjic-943	169	19	in	in	ADP
hjic-943	169	20	fig.j	fig.j	PROPN
hjic-943	169	21	.	.	PUNCT
hjic-943	170	1	let	let	VERB
hjic-943	170	2	the	the	DET
hjic-943	170	3	vessel	vessel	NOUN
hjic-943	170	4	be	be	AUX
hjic-943	170	5	perfectly	perfectly	ADV
hjic-943	170	6	stirred	stir	VERB
hjic-943	170	7	.	.	PUNCT
hjic-943	171	1	heat	heat	NOUN
hjic-943	171	2	is	be	AUX
hjic-943	171	3	transferred	transfer	VERB
hjic-943	171	4	to	to	ADP
hjic-943	171	5	the	the	DET
hjic-943	171	6	liquid	liquid	NOUN
hjic-943	171	7	using	use	VERB
hjic-943	171	8	a	a	DET
hjic-943	171	9	heater	heater	NOUN
hjic-943	171	10	.	.	PUNCT
hjic-943	172	1	the	the	DET
hjic-943	172	2	flow	flow	NOUN
hjic-943	172	3	rate	rate	NOUN
hjic-943	172	4	and	and	CCONJ
hjic-943	172	5	the	the	DET
hjic-943	172	6	enthalpy	enthalpy	NOUN
hjic-943	172	7	of	of	ADP
hjic-943	172	8	inlet	inlet	ADJ
hjic-943	172	9	stream	stream	NOUN
hjic-943	172	10	as	as	ADV
hjic-943	172	11	well	well	ADV
hjic-943	172	12	as	as	ADP
hjic-943	172	13	the	the	DET
hjic-943	172	14	flow	flow	NOUN
hjic-943	172	15	rate	rate	NOUN
hjic-943	172	16	of	of	ADP
hjic-943	172	17	the	the	DET
hjic-943	172	18	outlet	outlet	NOUN
hjic-943	172	19	stream	stream	NOUN
hjic-943	172	20	and	and	CCONJ
hjic-943	172	21	the	the	DET
hjic-943	172	22	heat	heat	NOUN
hjic-943	172	23	transfer	transfer	NOUN
hjic-943	172	24	rate	rate	NOUN
hjic-943	172	25	are	be	AUX
hjic-943	172	26	functions	function	NOUN
hjic-943	172	27	of	of	ADP
hjic-943	172	28	time	time	NOUN
hjic-943	172	29	.	.	PUNCT
hjic-943	173	1	65	65	NUM
hjic-943	173	2	th~	th~	PROPN
hjic-943	173	3	model	model	NOUN
hjic-943	173	4	equations	equation	NOUN
hjic-943	173	5	of	of	ADP
hjic-943	173	6	the	the	DET
hjic-943	173	7	above	above	ADJ
hjic-943	173	8	system	system	NOUN
hjic-943	173	9	are	be	AUX
hjic-943	173	10	the	the	DET
hjic-943	173	11	followmg	followmg	NOUN
hjic-943	173	12	:	:	PUNCT
hjic-943	173	13	m	m	VERB
hjic-943	173	14	'	'	PART
hjic-943	173	15	=	=	ADJ
hjic-943	173	16	-l+f	-l+f	VERB
hjic-943	173	17	(	(	PUNCT
hjic-943	173	18	19	19	NUM
hjic-943	173	19	)	)	PUNCT
hjic-943	173	20	u	u	NOUN
hjic-943	173	21	=	=	PROPN
hjic-943	173	22	-l·hl	-l·hl	PROPN
hjic-943	173	23	+	+	NOUN
hjic-943	173	24	f·hf	f·hf	ADJ
hjic-943	173	25	+	+	NOUN
hjic-943	173	26	q	q	X
hjic-943	173	27	(	(	PUNCT
hjic-943	173	28	20	20	NUM
hjic-943	173	29	)	)	PUNCT
hjic-943	173	30	hl	hl	NOUN
hjic-943	173	31	=	=	PROPN
hjic-943	173	32	f1	f1	PROPN
hjic-943	173	33	(	(	PUNCT
hjic-943	173	34	tl	tl	PROPN
hjic-943	173	35	,	,	PUNCT
hjic-943	173	36	p	p	NOUN
hjic-943	173	37	)	)	PUNCT
hjic-943	173	38	(	(	PUNCT
hjic-943	173	39	21	21	NUM
hjic-943	173	40	)	)	PUNCT
hjic-943	173	41	hf	hf	NOUN
hjic-943	173	42	=	=	SYM
hjic-943	173	43	fz(tf	fz(tf	PROPN
hjic-943	173	44	,	,	PUNCT
hjic-943	173	45	pf	pf	NOUN
hjic-943	173	46	)	)	PUNCT
hjic-943	173	47	(	(	PUNCT
hjic-943	173	48	22	22	NUM
hjic-943	173	49	)	)	PUNCT
hjic-943	173	50	u	u	NOUN
hjic-943	173	51	=	=	VERB
hjic-943	173	52	m·ul	m·ul	PROPN
hjic-943	173	53	(	(	PUNCT
hjic-943	173	54	23	23	NUM
hjic-943	173	55	)	)	PUNCT
hjic-943	173	56	ul	ul	NOUN
hjic-943	173	57	=	=	SYM
hjic-943	173	58	f3(hl	f3(hl	PROPN
hjic-943	173	59	,	,	PUNCT
hjic-943	173	60	p	p	NOUN
hjic-943	173	61	)	)	PUNCT
hjic-943	173	62	(	(	PUNCT
hjic-943	173	63	24	24	NUM
hjic-943	173	64	)	)	PUNCT
hjic-943	173	65	l	l	NOUN
hjic-943	173	66	=	=	SYM
hjic-943	173	67	f4	f4	PROPN
hjic-943	173	68	(	(	PUNCT
hjic-943	173	69	m	m	NOUN
hjic-943	173	70	)	)	PUNCT
hjic-943	173	71	(	(	PUNCT
hjic-943	173	72	25	25	NUM
hjic-943	173	73	)	)	PUNCT
hjic-943	173	74	herem	herem	PROPN
hjic-943	173	75	denotes	denote	VERB
hjic-943	173	76	the	the	DET
hjic-943	173	77	mass	mass	NOUN
hjic-943	173	78	,	,	PUNCT
hjic-943	173	79	u	u	NOUN
hjic-943	173	80	the	the	DET
hjic-943	173	81	internal	internal	ADJ
hjic-943	173	82	energy	energy	NOUN
hjic-943	173	83	,	,	PUNCT
hjic-943	173	84	q	q	NOUN
hjic-943	173	85	heat	heat	NOUN
hjic-943	173	86	transfer	transfer	NOUN
hjic-943	173	87	rate	rate	NOUN
hjic-943	173	88	,	,	PUNCT
hjic-943	173	89	f	f	PROPN
hjic-943	173	90	and	and	CCONJ
hjic-943	173	91	l	l	PROPN
hjic-943	173	92	inlet	inlet	NOUN
hjic-943	173	93	and	and	CCONJ
hjic-943	173	94	outlet	outlet	NOUN
hjic-943	173	95	mass	mass	PROPN
hjic-943	173	96	flow	flow	NOUN
hjic-943	173	97	rate	rate	NOUN
hjic-943	173	98	,	,	PUNCT
hjic-943	173	99	hf	hf	NOUN
hjic-943	173	100	and	and	CCONJ
hjic-943	173	101	hl	hl	X
hjic-943	173	102	specific	specific	ADJ
hjic-943	173	103	enthalpy	enthalpy	NOUN
hjic-943	173	104	of	of	ADP
hjic-943	173	105	inlet	inlet	NOUN
hjic-943	173	106	and	and	CCONJ
hjic-943	173	107	outlet	outlet	NOUN
hjic-943	173	108	flow~	flow~	PROPN
hjic-943	173	109	ul	ul	INTJ
hjic-943	173	110	specific	specific	ADJ
hjic-943	173	111	internal	internal	ADJ
hjic-943	173	112	energy	energy	NOUN
hjic-943	173	113	,	,	PUNCT
hjic-943	173	114	tftemperature	tftemperature	NOUN
hjic-943	173	115	of	of	ADP
hjic-943	173	116	inlet	inlet	ADJ
hjic-943	173	117	flow	flow	NOUN
hjic-943	173	118	,	,	PUNCT
hjic-943	173	119	pf	pf	NOUN
hjic-943	173	120	pressure	pressure	NOUN
hjic-943	173	121	of	of	ADP
hjic-943	173	122	inlet	inlet	ADJ
hjic-943	173	123	flow	flow	NOUN
hjic-943	173	124	,	,	PUNCT
hjic-943	173	125	tl	tl	PROPN
hjic-943	173	126	temperature	temperature	NOUN
hjic-943	173	127	in	in	ADP
hjic-943	173	128	the	the	DET
hjic-943	173	129	vessel	vessel	NOUN
hjic-943	173	130	,	,	PUNCT
hjic-943	173	131	p	p	ADJ
hjic-943	173	132	atmospheric	atmospheric	ADJ
hjic-943	173	133	pressure	pressure	NOUN
hjic-943	173	134	,	,	PUNCT
hjic-943	173	135	respectively	respectively	ADV
hjic-943	173	136	and	and	CCONJ
hjic-943	173	137	fi	fi	NOUN
hjic-943	173	138	,	,	PUNCT
hjic-943	173	139	f2	f2	PROPN
hjic-943	173	140	and	and	CCONJ
hjic-943	173	141	h	h	NOUN
hjic-943	173	142	are	be	AUX
hjic-943	173	143	given	give	VERB
hjic-943	173	144	functions	function	NOUN
hjic-943	173	145	.	.	PUNCT
hjic-943	174	1	the	the	DET
hjic-943	174	2	standard	standard	ADJ
hjic-943	174	3	form	form	NOUN
hjic-943	174	4	of	of	ADP
hjic-943	174	5	this	this	DET
hjic-943	174	6	model	model	NOUN
hjic-943	174	7	is	be	AUX
hjic-943	174	8	as	as	SCONJ
hjic-943	174	9	follows	follow	VERB
hjic-943	174	10	:	:	PUNCT
hjic-943	174	11	m	m	NOUN
hjic-943	174	12	=	=	NOUN
hjic-943	174	13	fm	fm	NOUN
hjic-943	174	14	'	'	PUNCT
hjic-943	174	15	(	(	PUNCT
hjic-943	174	16	26	26	NUM
hjic-943	174	17	)	)	PUNCT
hjic-943	174	18	u	u	NOUN
hjic-943	174	19	=	=	PROPN
hjic-943	174	20	ju	ju	NOUN
hjic-943	174	21	'	'	PUNCT
hjic-943	174	22	(	(	PUNCT
hjic-943	174	23	27	27	NUM
hjic-943	174	24	)	)	PUNCT
hjic-943	174	25	m	m	PROPN
hjic-943	174	26	'	'	PART
hjic-943	174	27	=	=	ADJ
hjic-943	174	28	-l+f	-l+f	VERB
hjic-943	174	29	(	(	PUNCT
hjic-943	174	30	28	28	NUM
hjic-943	174	31	)	)	PUNCT
hjic-943	174	32	u	u	NOUN
hjic-943	174	33	'	'	PUNCT
hjic-943	174	34	=	=	ADJ
hjic-943	174	35	-l·hl	-l·hl	PROPN
hjic-943	174	36	+	+	NOUN
hjic-943	174	37	f·hf	f·hf	ADJ
hjic-943	174	38	+	+	NOUN
hjic-943	174	39	q	q	X
hjic-943	174	40	(	(	PUNCT
hjic-943	174	41	29l	29l	NOUN
hjic-943	174	42	hl	hl	NOUN
hjic-943	174	43	=	=	SYM
hjic-943	174	44	f1(tl	f1(tl	PROPN
hjic-943	174	45	,	,	PUNCT
hjic-943	174	46	p	p	NOUN
hjic-943	174	47	)	)	PUNCT
hjic-943	174	48	(	(	PUNCT
hjic-943	174	49	30	30	NUM
hjic-943	174	50	)	)	PUNCT
hjic-943	174	51	h	h	NOUN
hjic-943	174	52	f	f	NOUN
hjic-943	174	53	=	=	PRON
hjic-943	174	54	fz	fz	PROPN
hjic-943	174	55	(	(	PUNCT
hjic-943	174	56	t	t	NOUN
hjic-943	174	57	f	f	X
hjic-943	174	58	'	'	X
hjic-943	174	59	p	p	NOUN
hjic-943	174	60	f	f	NOUN
hjic-943	174	61	)	)	PUNCT
hjic-943	174	62	(	(	PUNCT
hjic-943	174	63	31	31	NUM
hjic-943	174	64	)	)	PUNCT
hjic-943	174	65	u	u	NOUN
hjic-943	174	66	(	(	PUNCT
hjic-943	174	67	32	32	NUM
hjic-943	174	68	!	!	PUNCT
hjic-943	174	69	ul	ul	X
hjic-943	175	1	=	=	NOUN
hjic-943	175	2	m	m	NOUN
hjic-943	175	3	u~	u~	PROPN
hjic-943	175	4	=	=	PUNCT
hjic-943	175	5	f3(hl	f3(hl	PROPN
hjic-943	175	6	,	,	PUNCT
hjic-943	175	7	p	p	NOUN
hjic-943	175	8	)	)	PUNCT
hjic-943	175	9	(	(	PUNCT
hjic-943	175	10	33	33	NUM
hjic-943	175	11	)	)	PUNCT
hjic-943	175	12	*	*	PUNCT
hjic-943	176	1	s	s	X
hjic-943	176	2	=	=	X
hjic-943	176	3	o	o	X
hjic-943	176	4	(	(	PUNCT
hjic-943	176	5	34	34	NUM
hjic-943	176	6	)	)	PUNCT
hjic-943	176	7	s	s	PART
hjic-943	177	1	=	=	NOUN
hjic-943	177	2	ul	ul	NOUN
hjic-943	177	3	-ul	-ul	NOUN
hjic-943	177	4	,	,	PUNCT
hjic-943	177	5	l=	l=	ADJ
hjic-943	177	6	/	/	SYM
hjic-943	177	7	4	4	NUM
hjic-943	177	8	(	(	PUNCT
hjic-943	177	9	m	m	NOUN
hjic-943	177	10	)	)	PUNCT
hjic-943	177	11	(	(	PUNCT
hjic-943	177	12	35	35	NUM
hjic-943	177	13	}	}	PUNCT
hjic-943	177	14	introduction	introduction	NOUN
hjic-943	177	15	of	of	ADP
hjic-943	177	16	new	new	ADJ
hjic-943	177	17	variables	variable	NOUN
hjic-943	177	18	u	u	NOUN
hjic-943	177	19	;	;	PUNCT
hjic-943	177	20	~	~	PUNCT
hjic-943	177	21	s	s	X
hjic-943	177	22	and	and	CCONJ
hjic-943	177	23	the	the	DET
hjic-943	177	24	equation	equation	NOUN
hjic-943	177	25	s	s	PART
hjic-943	177	26	=	=	SYM
hjic-943	177	27	u	u	X
hjic-943	177	28	l	l	NOUN
hjic-943	177	29	u	u	NOUN
hjic-943	177	30	~.	~.	X
hjic-943	177	31	s	s	PART
hjic-943	177	32	=	=	NOUN
hjic-943	177	33	0	0	NUM
hjic-943	177	34	into	into	ADP
hjic-943	177	35	the	the	DET
hjic-943	177	36	original	original	ADJ
hjic-943	177	37	model	model	NOUN
hjic-943	177	38	guarantees	guarantee	VERB
hjic-943	177	39	that	that	SCONJ
hjic-943	177	40	all	all	DET
hjic-943	177	41	variables	variable	NOUN
hjic-943	177	42	on	on	ADP
hjic-943	177	43	the	the	DET
hjic-943	177	44	left	left	ADJ
hjic-943	177	45	-	-	PUNCT
hjic-943	177	46	hand	hand	NOUN
hjic-943	177	47	side	side	NOUN
hjic-943	177	48	of	of	ADP
hjic-943	177	49	the	the	DET
hjic-943	177	50	model	model	NOUN
hjic-943	177	51	are	be	AUX
hjic-943	177	52	different	different	ADJ
hjic-943	177	53	.	.	PUNCT
hjic-943	178	1	in	in	ADP
hjic-943	178	2	eq.(34	eq.(34	NOUN
hjic-943	178	3	)	)	PUNCT
hjic-943	178	4	the	the	DET
hjic-943	178	5	"	"	PUNCT
hjic-943	178	6	satellite	satellite	NOUN
hjic-943	178	7	..	..	PUNCT
hjic-943	178	8	notes	note	VERB
hjic-943	178	9	=	=	SYM
hjic-943	178	10	0	0	NUM
hjic-943	178	11	refers	refer	VERB
hjic-943	178	12	to	to	ADP
hjic-943	178	13	the	the	DET
hjic-943	178	14	fact	fact	NOUN
hjic-943	178	15	that	that	SCONJ
hjic-943	178	16	the	the	DET
hjic-943	178	17	value	value	NOUN
hjic-943	178	18	of	of	ADP
hjic-943	178	19	variable	variable	NOUN
hjic-943	178	20	s	s	PART
hjic-943	178	21	is	be	AUX
hjic-943	178	22	set	set	VERB
hjic-943	178	23	to	to	ADP
hjic-943	178	24	0	0	NUM
hjic-943	178	25	.	.	PUNCT
hjic-943	179	1	i.e.	i.e.	X
hjic-943	179	2	the	the	DET
hjic-943	179	3	variable	variable	ADJ
hjic-943	179	4	vertex	vertex	NOUN
hjic-943	179	5	s	s	PART
hjic-943	179	6	is	be	AUX
hjic-943	179	7	labeled	label	VERB
hjic-943	179	8	by	by	ADP
hjic-943	179	9	type	type	NOUN
hjic-943	179	10	<	<	X
hjic-943	179	11	g	g	PROPN
hjic-943	179	12	>	>	X
hjic-943	179	13	.	.	PUNCT
hjic-943	180	1	the	the	DET
hjic-943	180	2	representation	representation	NOUN
hjic-943	180	3	graph	graph	NOUN
hjic-943	180	4	of	of	ADP
hjic-943	180	5	the	the	DET
hjic-943	180	6	liquid	liquid	ADJ
hjic-943	180	7	tank	tank	NOUN
hjic-943	180	8	system	system	NOUN
hjic-943	180	9	is	be	AUX
hjic-943	180	10	shown	show	VERB
hjic-943	180	11	in	in	ADP
hjic-943	180	12	fig.4a	fig.4a	NOUN
hjic-943	180	13	.	.	PUNCT
hjic-943	181	1	we	we	PRON
hjic-943	181	2	indicate	indicate	VERB
hjic-943	181	3	differential	differential	ADJ
hjic-943	181	4	variables	variable	NOUN
hjic-943	181	5	on	on	ADP
hjic-943	181	6	the	the	DET
hjic-943	181	7	static	static	ADJ
hjic-943	181	8	graph	graph	NOUN
hjic-943	181	9	at	at	ADP
hjic-943	181	10	time	time	NOUN
hjic-943	181	11	step	step	NOUN
hjic-943	181	12	t+l	t+l	NUM
hjic-943	181	13	only	only	ADV
hjic-943	181	14	.	.	PUNCT
hjic-943	182	1	but	but	CCONJ
hjic-943	182	2	the	the	DET
hjic-943	182	3	structun~	structun~	NOUN
hjic-943	182	4	of	of	ADP
hjic-943	182	5	this	this	DET
hjic-943	182	6	graph	graph	NOUN
hjic-943	182	7	is	be	AUX
hjic-943	182	8	the	the	DET
hjic-943	182	9	same	same	ADJ
hjic-943	182	10	as	as	ADP
hjic-943	182	11	the	the	DET
hjic-943	182	12	structure	structure	NOUN
hjic-943	182	13	of	of	ADP
hjic-943	182	14	static	static	ADJ
hjic-943	182	15	graph	graph	NOUN
hjic-943	182	16	at	at	ADP
hjic-943	182	17	time	time	NOUN
hjic-943	182	18	step	step	NOUN
hjic-943	182	19	t.	t.	PROPN
hjic-943	182	20	66	66	NUM
hjic-943	183	1	p	p	NOUN
hjic-943	183	2	,	,	PUNCT
hjic-943	183	3	<	<	X
hjic-943	183	4	s	s	X
hjic-943	183	5	>	>	X
hjic-943	183	6	t	t	PROPN
hjic-943	183	7	•	•	NUM
hjic-943	183	8	•	•	ADP
hjic-943	183	9	a	a	DET
hjic-943	183	10	,	,	PUNCT
hjic-943	183	11	b	b	NOUN
hjic-943	183	12	,	,	PUNCT
hjic-943	183	13	m	m	PROPN
hjic-943	183	14	...	...	PUNCT
hjic-943	183	15	-----~	-----~	PUNCT
hjic-943	184	1	i	i	PRON
hjic-943	184	2	'	'	PUNCT
hjic-943	184	3	i	i	PRON
hjic-943	184	4	t+1	t+1	PROPN
hjic-943	184	5	fig	fig	VERB
hjic-943	184	6	a	a	DET
hjic-943	184	7	representation	representation	NOUN
hjic-943	184	8	of	of	ADP
hjic-943	184	9	model	model	NOUN
hjic-943	184	10	with	with	ADP
hjic-943	184	11	specification	specification	NOUN
hjic-943	184	12	i	i	PRON
hjic-943	184	13	in	in	ADP
hjic-943	184	14	example	example	NOUN
hjic-943	184	15	2	2	NUM
hjic-943	184	16	;	;	PUNCT
hjic-943	184	17	a	a	DET
hjic-943	184	18	,	,	PUNCT
hjic-943	184	19	representation	representation	NOUN
hjic-943	184	20	graph	graph	NOUN
hjic-943	184	21	;	;	PUNCT
hjic-943	184	22	b	b	NUM
hjic-943	184	23	,	,	PUNCT
hjic-943	184	24	reduced	reduce	VERB
hjic-943	184	25	graph	graph	NOUN
hjic-943	184	26	furthermore	furthermore	ADV
hjic-943	184	27	,	,	PUNCT
hjic-943	184	28	consider	consider	VERB
hjic-943	184	29	the	the	DET
hjic-943	184	30	following	follow	VERB
hjic-943	184	31	specification	specification	NOUN
hjic-943	184	32	.	.	PUNCT
hjic-943	185	1	specification	specification	NOUN
hjic-943	185	2	1	1	NUM
hjic-943	185	3	.	.	PUNCT
hjic-943	186	1	given	give	VERB
hjic-943	186	2	:	:	PUNCT
hjic-943	186	3	the	the	DET
hjic-943	186	4	properties	property	NOUN
hjic-943	186	5	of	of	ADP
hjic-943	186	6	the	the	DET
hjic-943	186	7	inlet	inlet	NOUN
hjic-943	186	8	flow	flow	NOUN
hjic-943	186	9	f	f	PROPN
hjic-943	186	10	,	,	PUNCT
hjic-943	186	11	tp	tp	NOUN
hjic-943	186	12	,	,	PUNCT
hjic-943	186	13	pf	pf	PROPN
hjic-943	186	14	and	and	CCONJ
hjic-943	186	15	the	the	DET
hjic-943	186	16	heat	heat	NOUN
hjic-943	186	17	transfer	transfer	NOUN
hjic-943	186	18	rate	rate	NOUN
hjic-943	186	19	q	q	NOUN
hjic-943	186	20	as	as	ADP
hjic-943	186	21	functions	function	NOUN
hjic-943	186	22	of	of	ADP
hjic-943	186	23	time	time	NOUN
hjic-943	186	24	;	;	PUNCT
hjic-943	186	25	the	the	DET
hjic-943	186	26	initial	initial	ADJ
hjic-943	186	27	values	value	NOUN
hjic-943	186	28	of	of	ADP
hjic-943	186	29	mass	mass	NOUN
hjic-943	186	30	and	and	CCONJ
hjic-943	186	31	internal	internal	ADJ
hjic-943	186	32	energy	energy	NOUN
hjic-943	186	33	m0	m0	NOUN
hjic-943	186	34	,	,	PUNCT
hjic-943	186	35	u0	u0	ADJ
hjic-943	186	36	and	and	CCONJ
hjic-943	186	37	the	the	DET
hjic-943	186	38	pressure	pressure	NOUN
hjic-943	186	39	p	p	NOUN
hjic-943	186	40	are	be	AUX
hjic-943	186	41	constants	constant	NOUN
hjic-943	186	42	;	;	PUNCT
hjic-943	186	43	to	to	PART
hjic-943	186	44	be	be	AUX
hjic-943	186	45	calculated	calculate	VERB
hjic-943	186	46	:	:	PUNCT
hjic-943	186	47	the	the	DET
hjic-943	186	48	mass	mass	PROPN
hjic-943	186	49	,	,	PUNCT
hjic-943	186	50	the	the	DET
hjic-943	186	51	internal	internal	ADJ
hjic-943	186	52	energy	energy	NOUN
hjic-943	186	53	and	and	CCONJ
hjic-943	186	54	temperature	temperature	NOUN
hjic-943	186	55	of	of	ADP
hjic-943	186	56	the	the	DET
hjic-943	186	57	liquid	liquid	NOUN
hjic-943	186	58	in	in	ADP
hjic-943	186	59	the	the	DET
hjic-943	186	60	vessel	vessel	NOUN
hjic-943	186	61	and	and	CCONJ
hjic-943	186	62	the	the	DET
hjic-943	186	63	outlet	outlet	NOUN
hjic-943	186	64	flow	flow	NOUN
hjic-943	186	65	rate	rate	NOUN
hjic-943	186	66	m	m	PROPN
hjic-943	186	67	,	,	PUNCT
hjic-943	186	68	u~	u~	PROPN
hjic-943	186	69	tl	tl	PROPN
hjic-943	186	70	,	,	PUNCT
hjic-943	186	71	l	l	NOUN
hjic-943	186	72	as	as	ADP
hjic-943	186	73	functions	function	NOUN
hjic-943	186	74	of	of	ADP
hjic-943	186	75	time	time	NOUN
hjic-943	186	76	.	.	PUNCT
hjic-943	187	1	it	it	PRON
hjic-943	187	2	can	can	AUX
hjic-943	187	3	be	be	AUX
hjic-943	187	4	shown	show	VERB
hjic-943	187	5	that	that	SCONJ
hjic-943	187	6	the	the	DET
hjic-943	187	7	differential	differential	ADJ
hjic-943	187	8	index	index	NOUN
hjic-943	187	9	of	of	ADP
hjic-943	187	10	this	this	DET
hjic-943	187	11	semi	semi	ADJ
hjic-943	187	12	-	-	ADJ
hjic-943	187	13	explicit	explicit	ADJ
hjic-943	187	14	dae	dae	NOUN
hjic-943	187	15	system	system	NOUN
hjic-943	187	16	is	be	AUX
hjic-943	187	17	equal	equal	ADJ
hjic-943	187	18	to	to	ADP
hjic-943	187	19	1	1	NUM
hjic-943	187	20	.	.	PUNCT
hjic-943	187	21	dynamic	dynamic	ADJ
hjic-943	187	22	degree	degree	NOUN
hjic-943	187	23	of	of	ADP
hjic-943	187	24	freedom	freedom	NOUN
hjic-943	187	25	is	be	AUX
hjic-943	187	26	2	2	NUM
hjic-943	187	27	.	.	NUM
hjic-943	187	28	,	,	PUNCT
hjic-943	187	29	so	so	ADV
hjic-943	187	30	initial	initial	ADJ
hjic-943	187	31	values	value	NOUN
hjic-943	187	32	of	of	ADP
hjic-943	187	33	mass	mass	NOUN
hjic-943	187	34	m	m	PROPN
hjic-943	187	35	and	and	CCONJ
hjic-943	187	36	internal	internal	ADJ
hjic-943	187	37	energy	energy	NOUN
hjic-943	187	38	u	u	NOUN
hjic-943	187	39	can	can	AUX
hjic-943	187	40	be	be	AUX
hjic-943	187	41	chosen	choose	VERB
hjic-943	187	42	independently	independently	ADV
hjic-943	187	43	.	.	PUNCT
hjic-943	188	1	the	the	DET
hjic-943	188	2	types	type	NOUN
hjic-943	188	3	of	of	ADP
hjic-943	188	4	variables	variable	NOUN
hjic-943	188	5	assigned	assign	VERB
hjic-943	188	6	corresponding	correspond	VERB
hjic-943	188	7	to	to	ADP
hjic-943	188	8	specification	specification	NOUN
hjic-943	188	9	1	1	NUM
hjic-943	188	10	are	be	AUX
hjic-943	188	11	shown	show	VERB
hjic-943	188	12	in	in	ADP
hjic-943	188	13	fig.4a	fig.4a	NOUN
hjic-943	188	14	.	.	PUNCT
hjic-943	189	1	the	the	DET
hjic-943	189	2	reduced	reduce	VERB
hjic-943	189	3	graph	graph	NOUN
hjic-943	189	4	according	accord	VERB
hjic-943	189	5	to	to	ADP
hjic-943	189	6	specification	specification	NOUN
hjic-943	189	7	1	1	NUM
hjic-943	189	8	is	be	AUX
hjic-943	189	9	shown	show	VERB
hjic-943	189	10	in	in	ADP
hjic-943	189	11	fig.4b	fig.4b	NOUN
hjic-943	189	12	.	.	PUNCT
hjic-943	190	1	having	having	AUX
hjic-943	190	2	produced	produce	VERB
hjic-943	190	3	reduced	reduced	ADJ
hjic-943	190	4	graph	graph	NOUN
hjic-943	190	5	,	,	PUNCT
hjic-943	190	6	the	the	DET
hjic-943	190	7	variable	variable	ADJ
hjic-943	190	8	classes	class	NOUN
hjic-943	190	9	related	relate	VERB
hjic-943	190	10	to	to	ADP
hjic-943	190	11	it	it	PRON
hjic-943	190	12	can	can	AUX
hjic-943	190	13	also	also	ADV
hjic-943	190	14	be	be	AUX
hjic-943	190	15	given	give	VERB
hjic-943	190	16	(	(	PUNCT
hjic-943	190	17	see	see	VERB
hjic-943	190	18	the	the	DET
hjic-943	190	19	general	general	ADJ
hjic-943	190	20	standard	standard	ADJ
hjic-943	190	21	form	form	NOUN
hjic-943	190	22	model	model	NOUN
hjic-943	190	23	(	(	PUNCT
hjic-943	190	24	1	1	NUM
hjic-943	190	25	)	)	PUNCT
hjic-943	190	26	~	~	PUNCT
hjic-943	190	27	(	(	PUNCT
hjic-943	190	28	2	2	NUM
hjic-943	190	29	)	)	PUNCT
hjic-943	190	30	)	)	PUNCT
hjic-943	190	31	as	as	SCONJ
hjic-943	190	32	follows	follow	VERB
hjic-943	190	33	:	:	PUNCT
hjic-943	190	34	(	(	PUNCT
hjic-943	190	35	36	36	NUM
hjic-943	190	36	)	)	PUNCT
hjic-943	190	37	y={s	y={s	PROPN
hjic-943	190	38	}	}	PUNCT
hjic-943	190	39	(	(	PUNCT
hjic-943	190	40	37	37	NUM
hjic-943	190	41	)	)	PUNCT
hjic-943	190	42	(	(	PUNCT
hjic-943	190	43	38	38	NUM
hjic-943	190	44	)	)	PUNCT
hjic-943	190	45	and	and	CCONJ
hjic-943	190	46	the	the	DET
hjic-943	190	47	existence	existence	NOUN
hjic-943	190	48	of	of	ADP
hjic-943	190	49	the	the	DET
hjic-943	190	50	menger	menger	NOUN
hjic-943	190	51	~	~	SYM
hjic-943	190	52	type	type	NOUN
hjic-943	190	53	complete	complete	ADJ
hjic-943	190	54	linking	linking	NOUN
hjic-943	190	55	can	can	AUX
hjic-943	190	56	be	be	AUX
hjic-943	190	57	investigated	investigate	VERB
hjic-943	190	58	.	.	PUNCT
hjic-943	191	1	it	it	PRON
hjic-943	191	2	can	can	AUX
hjic-943	191	3	be	be	AUX
hjic-943	191	4	seen	see	VERB
hjic-943	191	5	that	that	SCONJ
hjic-943	191	6	there	there	PRON
hjic-943	191	7	exists	exist	VERB
hjic-943	191	8	a	a	DET
hjic-943	191	9	menger	menger	NOUN
hjic-943	191	10	-	-	PUNCT
hjic-943	191	11	type	type	NOUN
hjic-943	191	12	complete	complete	ADJ
hjic-943	191	13	linking	linking	NOUN
hjic-943	191	14	on	on	ADP
hjic-943	191	15	the	the	DET
hjic-943	191	16	reduced	reduce	VERB
hjic-943	191	17	graph	graph	NOUN
hjic-943	191	18	hence	hence	ADV
hjic-943	191	19	the	the	DET
hjic-943	191	20	model	model	NOUN
hjic-943	191	21	is	be	AUX
hjic-943	191	22	conditionally	conditionally	ADV
hjic-943	191	23	structurauy	structurauy	ADJ
hjic-943	191	24	solvable	solvable	ADJ
hjic-943	191	25	.	.	PUNCT
hjic-943	192	1	t+1	t+1	PROPN
hjic-943	192	2	fig.s	fig.	NOUN
hjic-943	192	3	representation	representation	NOUN
hjic-943	192	4	graph	graph	NOUN
hjic-943	192	5	of	of	ADP
hjic-943	192	6	model	model	NOUN
hjic-943	192	7	with	with	ADP
hjic-943	192	8	specification	specification	NOUN
hjic-943	192	9	2	2	NUM
hjic-943	192	10	in	in	ADP
hjic-943	192	11	example	example	NOUN
hjic-943	192	12	2	2	NUM
hjic-943	192	13	next	next	ADV
hjic-943	192	14	let	let	VERB
hjic-943	192	15	us	we	PRON
hjic-943	192	16	consider	consider	VERB
hjic-943	192	17	the	the	DET
hjic-943	192	18	following	follow	VERB
hjic-943	192	19	specification	specification	NOUN
hjic-943	192	20	:	:	PUNCT
hjic-943	192	21	specification	specification	NOUN
hjic-943	192	22	2	2	NUM
hjic-943	192	23	.	.	PUNCT
hjic-943	193	1	given	give	VERB
hjic-943	193	2	:	:	PUNCT
hjic-943	193	3	f	f	X
hjic-943	193	4	,	,	PUNCT
hjic-943	193	5	tp	tp	NOUN
hjic-943	193	6	,	,	PUNCT
hjic-943	193	7	pp	pp	CCONJ
hjic-943	193	8	,	,	PUNCT
hjic-943	193	9	tl	tl	PROPN
hjic-943	193	10	as	as	ADP
hjic-943	193	11	a	a	DET
hjic-943	193	12	function	function	NOUN
hjic-943	193	13	of	of	ADP
hjic-943	193	14	time	time	NOUN
hjic-943	193	15	;	;	PUNCT
hjic-943	193	16	m0	m0	NOUN
hjic-943	193	17	,	,	PUNCT
hjic-943	193	18	u0	u0	ADJ
hjic-943	193	19	,	,	PUNCT
hjic-943	193	20	p	p	NOUN
hjic-943	193	21	constants	constant	NOUN
hjic-943	193	22	;	;	PUNCT
hjic-943	193	23	to	to	PART
hjic-943	193	24	be	be	AUX
hjic-943	193	25	calculated	calculate	VERB
hjic-943	193	26	:	:	PUNCT
hjic-943	193	27	the	the	DET
hjic-943	193	28	mass	mass	PROPN
hjic-943	193	29	,	,	PUNCT
hjic-943	193	30	the	the	DET
hjic-943	193	31	internal	internal	ADJ
hjic-943	193	32	energy	energy	NOUN
hjic-943	193	33	of	of	ADP
hjic-943	193	34	the	the	DET
hjic-943	193	35	liquid	liquid	NOUN
hjic-943	193	36	in	in	ADP
hjic-943	193	37	the	the	DET
hjic-943	193	38	vessel	vessel	NOUN
hjic-943	193	39	,	,	PUNCT
hjic-943	193	40	the	the	DET
hjic-943	193	41	heat	heat	NOUN
hjic-943	193	42	transfer	transfer	NOUN
hjic-943	193	43	rate	rate	NOUN
hjic-943	193	44	and	and	CCONJ
hjic-943	193	45	the	the	DET
hjic-943	193	46	outlet	outlet	NOUN
hjic-943	193	47	flow	flow	NOUN
hjic-943	193	48	rate	rate	PROPN
hjic-943	193	49	m	m	PROPN
hjic-943	193	50	,	,	PUNCT
hjic-943	193	51	u	u	NOUN
hjic-943	193	52	,	,	PUNCT
hjic-943	193	53	q	q	INTJ
hjic-943	193	54	,	,	PUNCT
hjic-943	193	55	l	l	NOUN
hjic-943	193	56	as	as	ADP
hjic-943	193	57	functions	function	NOUN
hjic-943	193	58	of	of	ADP
hjic-943	193	59	time	time	NOUN
hjic-943	193	60	.	.	PUNCT
hjic-943	194	1	it	it	PRON
hjic-943	194	2	is	be	AUX
hjic-943	194	3	easy	easy	ADJ
hjic-943	194	4	to	to	PART
hjic-943	194	5	show	show	VERB
hjic-943	194	6	that	that	SCONJ
hjic-943	194	7	the	the	DET
hjic-943	194	8	model	model	NOUN
hjic-943	194	9	with	with	ADP
hjic-943	194	10	specification	specification	NOUN
hjic-943	194	11	2	2	NUM
hjic-943	194	12	is	be	AUX
hjic-943	194	13	a	a	DET
hjic-943	194	14	semi	semi	ADJ
hjic-943	194	15	-	-	ADJ
hjic-943	194	16	explicit	explicit	ADJ
hjic-943	194	17	index	index	NOUN
hjic-943	194	18	2	2	NUM
hjic-943	194	19	model	model	NOUN
hjic-943	194	20	,	,	PUNCT
hjic-943	194	21	because	because	SCONJ
hjic-943	194	22	the	the	DET
hjic-943	194	23	unknown	unknown	ADJ
hjic-943	194	24	variable	variable	NOUN
hjic-943	194	25	q	q	NOUN
hjic-943	194	26	is	be	AUX
hjic-943	194	27	not	not	PART
hjic-943	194	28	present	present	ADJ
hjic-943	194	29	in	in	ADP
hjic-943	194	30	the	the	DET
hjic-943	194	31	algebraic	algebraic	ADJ
hjic-943	194	32	equations	equation	NOUN
hjic-943	194	33	,	,	PUNCT
hjic-943	194	34	so	so	ADV
hjic-943	194	35	two	two	NUM
hjic-943	194	36	differentiations	differentiation	NOUN
hjic-943	194	37	are	be	AUX
hjic-943	194	38	needed	need	VERB
hjic-943	194	39	to	to	PART
hjic-943	194	40	express	express	VERB
hjic-943	194	41	q	q	NOUN
hjic-943	194	42	'	'	NOUN
hjic-943	194	43	.	.	PUNCT
hjic-943	195	1	the	the	DET
hjic-943	195	2	dynamic	dynamic	ADJ
hjic-943	195	3	degree	degree	NOUN
hjic-943	195	4	of	of	ADP
hjic-943	195	5	freedom	freedom	NOUN
hjic-943	195	6	is	be	AUX
hjic-943	195	7	1	1	NUM
hjic-943	195	8	,	,	PUNCT
hjic-943	195	9	so	so	ADV
hjic-943	195	10	initial	initial	ADJ
hjic-943	195	11	values	value	NOUN
hjic-943	195	12	of	of	ADP
hjic-943	195	13	mass	mass	ADJ
hjic-943	195	14	and	and	CCONJ
hjic-943	195	15	internal	internal	ADJ
hjic-943	195	16	energy	energy	NOUN
hjic-943	195	17	can	can	AUX
hjic-943	195	18	not	not	PART
hjic-943	195	19	be	be	AUX
hjic-943	195	20	chosen	choose	VERB
hjic-943	195	21	independently	independently	ADV
hjic-943	195	22	.	.	PUNCT
hjic-943	196	1	the	the	DET
hjic-943	196	2	types	type	NOUN
hjic-943	196	3	of	of	ADP
hjic-943	196	4	variables	variable	NOUN
hjic-943	196	5	which	which	PRON
hjic-943	196	6	(	(	PUNCT
hjic-943	196	7	}	}	PUNCT
hjic-943	196	8	.fe	.fe	PUNCT
hjic-943	196	9	assigned	assign	VERB
hjic-943	196	10	corresponding	correspond	VERB
hjic-943	196	11	to	to	ADP
hjic-943	196	12	specification	specification	NOUN
hjic-943	196	13	2	2	NUM
hjic-943	196	14	are	be	AUX
hjic-943	196	15	shown	show	VERB
hjic-943	196	16	in	in	ADP
hjic-943	196	17	fig.5	fig.5	PROPN
hjic-943	196	18	.	.	PUNCT
hjic-943	197	1	based	base	VERB
hjic-943	197	2	on	on	ADP
hjic-943	197	3	the	the	DET
hjic-943	197	4	structure	structure	NOUN
hjic-943	197	5	of	of	ADP
hjic-943	197	6	the	the	DET
hjic-943	197	7	representation	representation	NOUN
hjic-943	197	8	graph	graph	NOUN
hjic-943	197	9	on	on	ADP
hjic-943	197	10	fig.5	fig.5	NOUN
hjic-943	197	11	the	the	DET
hjic-943	197	12	following	follow	VERB
hjic-943	197	13	structural	structural	ADJ
hjic-943	197	14	solvability	solvability	NOUN
hjic-943	197	15	properties	property	NOUN
hjic-943	197	16	can	can	AUX
hjic-943	197	17	be	be	AUX
hjic-943	197	18	determined	determine	VERB
hjic-943	197	19	.	.	PUNCT
hjic-943	198	1	l.	l.	PROPN
hjic-943	198	2	the	the	DET
hjic-943	198	3	standard	standard	ADJ
hjic-943	198	4	form	form	NOUN
hjic-943	198	5	model	model	NOUN
hjic-943	198	6	is	be	AUX
hjic-943	198	7	not	not	PART
hjic-943	198	8	structurally	structurally	ADV
hjic-943	198	9	solvable	solvable	ADJ
hjic-943	198	10	.	.	PUNCT
hjic-943	199	1	(	(	PUNCT
hjic-943	199	2	there	there	PRON
hjic-943	199	3	is	be	VERB
hjic-943	199	4	no	no	DET
hjic-943	199	5	menger	menger	NOUN
hjic-943	199	6	-	-	PUNCT
hjic-943	199	7	type	type	NOUN
hjic-943	199	8	complete	complete	ADJ
hjic-943	199	9	linking	linking	NOUN
hjic-943	199	10	on	on	ADP
hjic-943	199	11	the	the	DET
hjic-943	199	12	graph	graph	NOUN
hjic-943	199	13	.	.	PUNCT
hjic-943	199	14	)	)	PUNCT
hjic-943	200	1	2	2	X
hjic-943	200	2	.	.	X
hjic-943	200	3	there	there	PRON
hjic-943	200	4	are	be	VERB
hjic-943	200	5	an	an	DET
hjic-943	200	6	overspecified	overspecified	ADJ
hjic-943	200	7	part	part	NOUN
hjic-943	200	8	and	and	CCONJ
hjic-943	200	9	an	an	DET
hjic-943	200	10	underspecijied	underspecijied	ADJ
hjic-943	200	11	part	part	NOUN
hjic-943	200	12	on	on	ADP
hjic-943	200	13	the	the	DET
hjic-943	200	14	representation	representation	NOUN
hjic-943	200	15	graph	graph	NOUN
hjic-943	200	16	.	.	PUNCT
hjic-943	201	1	the	the	DET
hjic-943	201	2	overspecified	overspecified	ADJ
hjic-943	201	3	part	part	NOUN
hjic-943	201	4	indicates	indicate	VERB
hjic-943	201	5	the	the	DET
hjic-943	201	6	fact	fact	NOUN
hjic-943	201	7	that	that	SCONJ
hjic-943	201	8	the	the	DET
hjic-943	201	9	initial	initial	ADJ
hjic-943	201	10	values	value	NOUN
hjic-943	201	11	of	of	ADP
hjic-943	201	12	the	the	DET
hjic-943	201	13	111odel	111odel	PROPN
hjic-943	201	14	can	can	AUX
hjic-943	201	15	not	not	PART
hjic-943	201	16	be	be	AUX
hjic-943	201	17	chosen	choose	VERB
hjic-943	201	18	independently	independently	ADV
hjic-943	201	19	.	.	PUNCT
hjic-943	202	1	the	the	DET
hjic-943	202	2	underspecified	underspecified	ADJ
hjic-943	202	3	part	part	NOUN
hjic-943	202	4	q	q	X
hjic-943	202	5	~	~	PUNCT
hjic-943	202	6	u	u	NOUN
hjic-943	202	7	'	'	PART
hjic-943	202	8	indicates	indicate	VERB
hjic-943	202	9	,	,	PUNCT
hjic-943	202	10	that	that	PRON
hjic-943	202	11	q	q	NOUN
hjic-943	202	12	can	can	AUX
hjic-943	202	13	not	not	PART
hjic-943	202	14	be	be	AUX
hjic-943	202	15	calculated	calculate	VERB
hjic-943	202	16	from	from	ADP
hjic-943	202	17	the	the	DET
hjic-943	202	18	algebraic	algebraic	ADJ
hjic-943	202	19	equations	equation	NOUN
hjic-943	202	20	,	,	PUNCT
hjic-943	202	21	so	so	SCONJ
hjic-943	202	22	the	the	DET
hjic-943	202	23	index	index	NOUN
hjic-943	202	24	of	of	ADP
hjic-943	202	25	the	the	DET
hjic-943	202	26	model	model	NOUN
hjic-943	202	27	is	be	AUX
hjic-943	202	28	>	>	X
hjic-943	202	29	1	1	NUM
hjic-943	202	30	.	.	PUNCT
hjic-943	203	1	the	the	DET
hjic-943	203	2	following	follow	VERB
hjic-943	203	3	theorem	theorem	NOUN
hjic-943	203	4	holds	hold	VERB
hjic-943	203	5	generally	generally	ADV
hjic-943	203	6	[	[	X
hjic-943	203	7	7	7	NUM
hjic-943	203	8	]	]	PUNCT
hjic-943	203	9	.	.	PUNCT
hjic-943	204	1	theorem	theorem	VERB
hjic-943	204	2	:	:	PUNCT
hjic-943	204	3	consider	consider	VERB
hjic-943	204	4	a	a	DET
hjic-943	204	5	dynamic	dynamic	ADJ
hjic-943	204	6	process	process	NOUN
hjic-943	204	7	model	model	NOUN
hjic-943	204	8	m	m	VERB
hjic-943	204	9	in	in	ADP
hjic-943	204	10	the	the	DET
hjic-943	204	11	standard	standard	ADJ
hjic-943	204	12	form	form	NOUN
hjic-943	204	13	described	describe	VERB
hjic-943	204	14	by	by	ADP
hjic-943	204	15	a	a	DET
hjic-943	204	16	semi	semi	ADJ
hjic-943	204	17	-	-	ADJ
hjic-943	204	18	explicit	explicit	ADJ
hjic-943	204	19	dae	dae	NOUN
hjic-943	204	20	system	system	NOUN
hjic-943	204	21	.	.	PUNCT
hjic-943	205	1	assume	assume	VERB
hjic-943	205	2	that	that	SCONJ
hjic-943	205	3	the	the	DET
hjic-943	205	4	generality	generality	NOUN
hjic-943	205	5	assumption	assumption	NOUN
hjic-943	205	6	ga	ga	PROPN
hjic-943	205	7	is	be	AUX
hjic-943	205	8	true	true	ADJ
hjic-943	205	9	.	.	PUNCT
hjic-943	206	1	then	then	ADV
hjic-943	206	2	the	the	DET
hjic-943	206	3	differential	differential	ADJ
hjic-943	206	4	index	index	NOUN
hjic-943	206	5	of	of	ADP
hjic-943	206	6	m	m	PROPN
hjic-943	206	7	is	be	AUX
hjic-943	206	8	equal	equal	ADJ
hjic-943	206	9	to	to	ADP
hjic-943	206	10	1	1	NUM
hjic-943	206	11	if	if	SCONJ
hjic-943	206	12	and	and	CCONJ
hjic-943	206	13	only	only	ADV
hjic-943	206	14	if	if	SCONJ
hjic-943	206	15	there	there	PRON
hjic-943	206	16	exists	exist	VERB
hjic-943	206	17	a	a	DET
hjic-943	206	18	menger	menger	NOUN
hjic-943	206	19	-	-	PUNCT
hjic-943	206	20	type	type	NOUN
hjic-943	206	21	complete	complete	ADJ
hjic-943	206	22	linking	linking	NOUN
hjic-943	206	23	on	on	ADP
hjic-943	206	24	the	the	DET
hjic-943	206	25	reduced	reduce	VERB
hjic-943	206	26	graph	graph	NOUN
hjic-943	206	27	at	at	ADP
hjic-943	206	28	any	any	DET
hjic-943	206	29	time	time	NOUN
hjic-943	206	30	step	step	NOUN
hjic-943	206	31	t.	t.	NOUN
hjic-943	206	32	consequence	consequence	NOUN
hjic-943	206	33	:	:	PUNCT
hjic-943	206	34	under	under	ADP
hjic-943	206	35	the	the	DET
hjic-943	206	36	assumptions	assumption	NOUN
hjic-943	206	37	of	of	ADP
hjic-943	206	38	theorem	theorem	NOUN
hjic-943	206	39	above	above	ADP
hjic-943	206	40	the	the	DET
hjic-943	206	41	following	follow	VERB
hjic-943	206	42	statement	statement	NOUN
hjic-943	206	43	holds	hold	VERB
hjic-943	206	44	.	.	PUNCT
hjic-943	207	1	if	if	SCONJ
hjic-943	207	2	the	the	DET
hjic-943	207	3	differential	differential	ADJ
hjic-943	207	4	index	index	NOUN
hjic-943	207	5	of	of	ADP
hjic-943	207	6	m	m	PROPN
hjic-943	207	7	is	be	AUX
hjic-943	207	8	greater	great	ADJ
hjic-943	207	9	than	than	ADP
hjic-943	207	10	1	1	NUM
hjic-943	207	11	then	then	ADV
hjic-943	207	12	there	there	PRON
hjic-943	207	13	is	be	VERB
hjic-943	207	14	no	no	DET
hjic-943	207	15	menger­	menger­	NOUN
hjic-943	207	16	type	type	NOUN
hjic-943	207	17	complete	complete	ADJ
hjic-943	207	18	linking	linking	NOUN
hjic-943	207	19	on	on	ADP
hjic-943	207	20	the	the	DET
hjic-943	207	21	static	static	ADJ
hjic-943	207	22	graph	graph	NOUN
hjic-943	207	23	at	at	ADP
hjic-943	207	24	any	any	DET
hjic-943	207	25	time	time	NOUN
hjic-943	207	26	step	step	NOUN
hjic-943	207	27	t.	t.	NOUN
hjic-943	207	28	the	the	DET
hjic-943	207	29	properties	property	NOUN
hjic-943	207	30	of	of	ADP
hjic-943	207	31	a	a	DET
hjic-943	207	32	static	static	ADJ
hjic-943	207	33	graph	graph	NOUN
hjic-943	207	34	of	of	ADP
hjic-943	207	35	a	a	DET
hjic-943	207	36	dynamic	dynamic	ADJ
hjic-943	207	37	model	model	NOUN
hjic-943	207	38	which	which	PRON
hjic-943	207	39	has	have	VERB
hjic-943	207	40	differential	differential	ADJ
hjic-943	207	41	index	index	NOUN
hjic-943	207	42	>	>	X
hjic-943	207	43	1	1	NUM
hjic-943	207	44	are	be	AUX
hjic-943	207	45	as	as	SCONJ
hjic-943	207	46	follows	follow	VERB
hjic-943	207	47	.	.	PUNCT
hjic-943	208	1	1	1	X
hjic-943	208	2	.	.	X
hjic-943	209	1	the	the	DET
hjic-943	209	2	fact	fact	NOUN
hjic-943	209	3	that	that	SCONJ
hjic-943	209	4	the	the	DET
hjic-943	209	5	initial	initial	ADJ
hjic-943	209	6	values	value	NOUN
hjic-943	209	7	of	of	ADP
hjic-943	209	8	integral	integral	ADJ
hjic-943	209	9	variables	variable	NOUN
hjic-943	209	10	can	can	AUX
hjic-943	209	11	not	not	PART
hjic-943	209	12	be	be	AUX
hjic-943	209	13	chosen	choose	VERB
hjic-943	209	14	independently	independently	ADV
hjic-943	209	15	results	result	NOUN
hjic-943	209	16	in	in	ADP
hjic-943	209	17	an	an	DET
hjic-943	209	18	overspecified	overspecified	ADJ
hjic-943	209	19	part	part	NOUN
hjic-943	209	20	on	on	ADP
hjic-943	209	21	the	the	DET
hjic-943	209	22	graph	graph	NOUN
hjic-943	209	23	.	.	PUNCT
hjic-943	210	1	this	this	DET
hjic-943	210	2	situation	situation	NOUN
hjic-943	210	3	can	can	AUX
hjic-943	210	4	be	be	AUX
hjic-943	210	5	easily	easily	ADV
hjic-943	210	6	shown	show	VERB
hjic-943	210	7	by	by	ADP
hjic-943	210	8	assignment	assignment	NOUN
hjic-943	210	9	of	of	ADP
hjic-943	210	10	types	type	NOUN
hjic-943	210	11	to	to	PART
hjic-943	210	12	vertices	vertice	VERB
hjic-943	210	13	corresponding	correspond	VERB
hjic-943	210	14	to	to	ADP
hjic-943	210	15	the	the	DET
hjic-943	210	16	model	model	NOUN
hjic-943	210	17	specification	specification	NOUN
hjic-943	210	18	.	.	PUNCT
hjic-943	211	1	there	there	PRON
hjic-943	211	2	is	be	VERB
hjic-943	211	3	an	an	DET
hjic-943	211	4	overspecified	overspecified	ADJ
hjic-943	211	5	part	part	NOUN
hjic-943	211	6	on	on	ADP
hjic-943	211	7	the	the	DET
hjic-943	211	8	graph	graph	NOUN
hjic-943	211	9	if	if	SCONJ
hjic-943	211	10	a	a	DET
hjic-943	211	11	vertex	vertex	NOUN
hjic-943	211	12	labeled	label	VERB
hjic-943	211	13	by	by	ADP
hjic-943	211	14	type	type	NOUN
hjic-943	211	15	<	<	X
hjic-943	211	16	g	g	X
hjic-943	211	17	>	>	X
hjic-943	211	18	can	can	AUX
hjic-943	211	19	also	also	ADV
hjic-943	211	20	be	be	AUX
hjic-943	211	21	labeled	label	VERB
hjic-943	211	22	secondarily	secondarily	ADV
hjic-943	211	23	or	or	CCONJ
hjic-943	211	24	tertiarily	tertiarily	ADV
hjic-943	211	25	or	or	CCONJ
hjic-943	211	26	etc	etc	X
hjic-943	211	27	.	.	X
hjic-943	211	28	by	by	ADP
hjic-943	211	29	type	type	NOUN
hjic-943	211	30	<	<	X
hjic-943	211	31	s	s	NOUN
hjic-943	211	32	>	>	X
hjic-943	211	33	.	.	PROPN
hjic-943	212	1	2	2	X
hjic-943	212	2	.	.	X
hjic-943	212	3	non	non	ADJ
hjic-943	212	4	-	-	NOUN
hjic-943	212	5	singularity	singularity	NOUN
hjic-943	212	6	of	of	ADP
hjic-943	212	7	gz2	gz2	NOUN
hjic-943	212	8	results	result	NOUN
hjic-943	212	9	in	in	ADP
hjic-943	212	10	an	an	DET
hjic-943	212	11	underspecified	underspecified	ADJ
hjic-943	212	12	part	part	NOUN
hjic-943	212	13	on	on	ADP
hjic-943	212	14	the	the	DET
hjic-943	212	15	graph	graph	NOUN
hjic-943	212	16	.	.	PUNCT
hjic-943	213	1	in	in	ADP
hjic-943	213	2	this	this	DET
hjic-943	213	3	part	part	NOUN
hjic-943	213	4	those	those	DET
hjic-943	213	5	algebraic	algebraic	ADJ
hjic-943	213	6	variables	variable	NOUN
hjic-943	213	7	appear	appear	VERB
hjic-943	213	8	which	which	PRON
hjic-943	213	9	can	can	AUX
hjic-943	213	10	not	not	PART
hjic-943	213	11	be	be	AUX
hjic-943	213	12	calculated	calculate	VERB
hjic-943	213	13	from	from	ADP
hjic-943	213	14	algebraic	algebraic	ADJ
hjic-943	213	15	equations	equation	NOUN
hjic-943	213	16	and	and	CCONJ
hjic-943	213	17	those	those	DET
hjic-943	213	18	differential	differential	ADJ
hjic-943	213	19	variables	variable	NOUN
hjic-943	213	20	which	which	PRON
hjic-943	213	21	we	we	PRON
hjic-943	213	22	want	want	VERB
hjic-943	213	23	to	to	PART
hjic-943	213	24	calculate	calculate	VERB
hjic-943	213	25	from	from	ADP
hjic-943	213	26	them	they	PRON
hjic-943	213	27	.	.	PUNCT
hjic-943	214	1	there	there	PRON
hjic-943	214	2	is	be	VERB
hjic-943	214	3	a	a	DET
hjic-943	214	4	natural	natural	ADJ
hjic-943	214	5	method	method	NOUN
hjic-943	214	6	for	for	ADP
hjic-943	214	7	index	index	NOUN
hjic-943	214	8	reduction	reduction	NOUN
hjic-943	214	9	suggested	suggest	VERB
hjic-943	214	10	by	by	ADP
hjic-943	214	11	the	the	DET
hjic-943	214	12	structure	structure	NOUN
hjic-943	214	13	of	of	ADP
hjic-943	214	14	the	the	DET
hjic-943	214	15	representation	representation	NOUN
hjic-943	214	16	graph	graph	NOUN
hjic-943	214	17	of	of	ADP
hjic-943	214	18	semi	semi	ADJ
hjic-943	214	19	-	-	ADJ
hjic-943	214	20	explicit	explicit	ADJ
hjic-943	214	21	dab	dab	NOUN
hjic-943	214	22	-	-	PUNCT
hjic-943	214	23	systems	system	NOUN
hjic-943	214	24	.	.	PUNCT
hjic-943	214	25	example	example	NOUN
hjic-943	214	26	2	2	NUM
hjic-943	214	27	(	(	PUNCT
hjic-943	214	28	continued	continue	VERB
hjic-943	214	29	)	)	PUNCT
hjic-943	214	30	.	.	PUNCT
hjic-943	215	1	consider	consider	VERB
hjic-943	215	2	example	example	NOUN
hjic-943	215	3	2	2	NUM
hjic-943	215	4	with	with	ADP
hjic-943	215	5	specification	specification	NOUN
hjic-943	215	6	2	2	NUM
hjic-943	215	7	.	.	PUNCT
hjic-943	216	1	this	this	DET
hjic-943	216	2	model	model	NOUN
hjic-943	216	3	has	have	AUX
hjic-943	216	4	differential	differential	ADJ
hjic-943	216	5	index	index	NOUN
hjic-943	216	6	2	2	NUM
hjic-943	216	7	.	.	PUNCT
hjic-943	216	8	modify	modify	VERB
hjic-943	216	9	the	the	DET
hjic-943	216	10	standard	standard	ADJ
hjic-943	216	11	form	form	NOUN
hjic-943	216	12	of	of	ADP
hjic-943	216	13	the	the	DET
hjic-943	216	14	model	model	NOUN
hjic-943	216	15	as	as	SCONJ
hjic-943	216	16	follows	follow	VERB
hjic-943	216	17	:	:	PUNCT
hjic-943	216	18	instead	instead	ADV
hjic-943	216	19	of	of	ADP
hjic-943	216	20	equation	equation	NOUN
hjic-943	216	21	_	_	PUNCT
hjic-943	217	1	u	u	NOUN
hjic-943	217	2	=	=	PUNCT
hjic-943	217	3	j	j	PROPN
hjic-943	217	4	u	u	NOUN
hjic-943	217	5	'	'	PART
hjic-943	217	6	introduce	introduce	VERB
hjic-943	217	7	the	the	DET
hjic-943	217	8	following	follow	VERB
hjic-943	217	9	equation	equation	NOUN
hjic-943	217	10	:	:	PUNCT
hjic-943	217	11	(	(	PUNCT
hjic-943	217	12	39	39	NUM
hjic-943	217	13	)	)	PUNCT
hjic-943	217	14	where	where	SCONJ
hjic-943	217	15	lf	lf	INTJ
hjic-943	217	16	and	and	CCONJ
hjic-943	217	17	[	[	X
hjic-943	217	18	j+i	j+i	NUM
hjic-943	217	19	denote	denote	VERB
hjic-943	217	20	the	the	DET
hjic-943	217	21	value	value	NOUN
hjic-943	217	22	of	of	ADP
hjic-943	217	23	internal	internal	ADJ
hjic-943	217	24	energy	energy	NOUN
hjic-943	217	25	u	u	NOUN
hjic-943	217	26	at	at	ADP
hjic-943	217	27	time	time	NOUN
hjic-943	217	28	step	step	NOUN
hjic-943	217	29	t	t	PROPN
hjic-943	217	30	and	and	CCONJ
hjic-943	217	31	t+l	t+l	NUM
hjic-943	217	32	,	,	PUNCT
hjic-943	217	33	respectively	respectively	ADV
hjic-943	217	34	.	.	PUNCT
hjic-943	218	1	this	this	DET
hjic-943	218	2	equation	equation	NOUN
hjic-943	218	3	corresponds	correspond	VERB
hjic-943	218	4	to	to	ADP
hjic-943	218	5	numerical	numerical	ADJ
hjic-943	218	6	derivation	derivation	NOUN
hjic-943	218	7	so	so	SCONJ
hjic-943	218	8	if	if	SCONJ
hjic-943	218	9	we	we	PRON
hjic-943	218	10	get	get	VERB
hjic-943	218	11	the	the	DET
hjic-943	218	12	derivative	derivative	ADJ
hjic-943	218	13	u	u	NOUN
hjic-943	218	14	'	'	PUNCT
hjic-943	218	15	by	by	ADP
hjic-943	218	16	numerical	numerical	ADJ
hjic-943	218	17	derivation	derivation	NOUN
hjic-943	218	18	we	we	PRON
hjic-943	218	19	can	can	AUX
hjic-943	218	20	calculate	calculate	VERB
hjic-943	218	21	qfromit	qfromit	NOUN
hjic-943	218	22	.	.	PUNCT
hjic-943	219	1	according	accord	VERB
hjic-943	219	2	to	to	ADP
hjic-943	219	3	the	the	DET
hjic-943	219	4	above	above	ADJ
hjic-943	219	5	transformation	transformation	NOUN
hjic-943	219	6	of	of	ADP
hjic-943	219	7	the	the	DET
hjic-943	219	8	standard	standard	ADJ
hjic-943	219	9	form	form	NOUN
hjic-943	219	10	,	,	PUNCT
hjic-943	219	11	let	let	VERB
hjic-943	219	12	the	the	DET
hjic-943	219	13	modified	modify	VERB
hjic-943	219	14	standard	standard	ADJ
hjic-943	219	15	form	form	NOUN
hjic-943	219	16	of	of	ADP
hjic-943	219	17	model	model	NOUN
hjic-943	219	18	of	of	ADP
hjic-943	219	19	example	example	NOUN
hjic-943	219	20	2	2	NUM
hjic-943	219	21	be	be	AUX
hjic-943	219	22	the	the	DET
hjic-943	219	23	following	following	NOUN
hjic-943	219	24	:	:	PUNCT
hjic-943	219	25	m	m	VERB
hjic-943	219	26	'	'	PART
hjic-943	219	27	=	=	ADJ
hjic-943	219	28	-l+f	-l+f	PUNCT
hjic-943	219	29	s	s	PROPN
hjic-943	219	30	=	=	NOUN
hjic-943	219	31	u	u	NOUN
hjic-943	219	32	·	·	PUNCT
hjic-943	219	33	-u·•	-u·•	X
hjic-943	219	34	,	,	PUNCT
hjic-943	219	35	s	s	NOUN
hjic-943	219	36	=	=	X
hjic-943	219	37	o	o	X
hjic-943	219	38	(	(	PUNCT
hjic-943	219	39	40	40	NUM
hjic-943	219	40	)	)	PUNCT
hjic-943	219	41	{	{	PUNCT
hjic-943	219	42	41	41	NUM
hjic-943	219	43	)	)	PUNCT
hjic-943	219	44	(	(	PUNCT
hjic-943	219	45	42	42	NUM
hjic-943	219	46	)	)	PUNCT
hjic-943	219	47	(	(	PUNCT
hjic-943	219	48	43	43	NUM
hjic-943	219	49	)	)	PUNCT
hjic-943	219	50	(	(	PUNCT
hjic-943	219	51	44	44	NUM
hjic-943	219	52	)	)	PUNCT
hjic-943	219	53	(	(	PUNCT
hjic-943	219	54	45	45	NUM
hjic-943	219	55	)	)	PUNCT
hjic-943	219	56	(	(	PUNCT
hjic-943	219	57	46	46	NUM
hjic-943	219	58	)	)	PUNCT
hjic-943	219	59	(	(	PUNCT
hjic-943	219	60	47	47	NUM
hjic-943	219	61	)	)	PUNCT
hjic-943	219	62	67	67	NUM
hjic-943	220	1	t+1	t+1	NUM
hjic-943	220	2	q	q	PROPN
hjic-943	220	3	p~	p~	PROPN
hjic-943	220	4	_	_	PUNCT
hjic-943	220	5	j	j	NOUN
hjic-943	220	6	'	'	PUNCT
hjic-943	220	7	-'-"""-<$	-'-"""-<$	X
hjic-943	220	8	>	>	X
hjic-943	221	1	_	_	PUNCT
hjic-943	221	2	_	_	PUNCT
hjic-943	222	1	a	a	DET
hjic-943	222	2	,	,	PUNCT
hjic-943	222	3	b	b	NOUN
hjic-943	222	4	,	,	PUNCT
hjic-943	222	5	fig.6	fig.6	PROPN
hjic-943	222	6	representation	representation	NOUN
hjic-943	222	7	of	of	ADP
hjic-943	222	8	modified	modified	ADJ
hjic-943	222	9	model	model	NOUN
hjic-943	222	10	in	in	ADP
hjic-943	222	11	example	example	NOUN
hjic-943	222	12	2	2	NUM
hjic-943	222	13	;	;	PUNCT
hjic-943	222	14	a	a	DET
hjic-943	222	15	,	,	PUNCT
hjic-943	222	16	representation	representation	NOUN
hjic-943	222	17	graph	graph	NOUN
hjic-943	222	18	;	;	PUNCT
hjic-943	222	19	b	b	NUM
hjic-943	222	20	,	,	PUNCT
hjic-943	222	21	reduced	reduce	VERB
hjic-943	222	22	graph	graph	NOUN
hjic-943	222	23	(	(	PUNCT
hjic-943	222	24	48	48	NUM
hjic-943	222	25	)	)	PUNCT
hjic-943	222	26	(	(	PUNCT
hjic-943	222	27	49	49	NUM
hjic-943	222	28	)	)	PUNCT
hjic-943	222	29	during	during	ADP
hjic-943	222	30	the	the	DET
hjic-943	222	31	modification	modification	NOUN
hjic-943	222	32	the	the	DET
hjic-943	222	33	internal	internal	ADJ
hjic-943	222	34	energy	energy	NOUN
hjic-943	222	35	u	u	NOUN
hjic-943	222	36	turns	turn	VERB
hjic-943	222	37	from	from	ADP
hjic-943	222	38	a	a	DET
hjic-943	222	39	differential	differential	ADJ
hjic-943	222	40	variable	variable	NOUN
hjic-943	222	41	into	into	ADP
hjic-943	222	42	an	an	DET
hjic-943	222	43	algebraic	algebraic	ADJ
hjic-943	222	44	variable	variable	NOUN
hjic-943	222	45	and	and	CCONJ
hjic-943	222	46	u	u	NOUN
hjic-943	222	47	'	'	PUNCT
hjic-943	222	48	turns	turn	VERB
hjic-943	222	49	from	from	ADP
hjic-943	222	50	a	a	DET
hjic-943	222	51	derivative	derivative	ADJ
hjic-943	222	52	variable	variable	NOUN
hjic-943	222	53	into	into	ADP
hjic-943	222	54	an	an	DET
hjic-943	222	55	algebraic	algebraic	ADJ
hjic-943	222	56	one	one	NUM
hjic-943	222	57	.	.	PUNCT
hjic-943	223	1	an	an	DET
hjic-943	223	2	important	important	ADJ
hjic-943	223	3	consequence	consequence	NOUN
hjic-943	223	4	of	of	ADP
hjic-943	223	5	the	the	DET
hjic-943	223	6	modification	modification	NOUN
hjic-943	223	7	is	be	AUX
hjic-943	223	8	that	that	SCONJ
hjic-943	223	9	there	there	PRON
hjic-943	223	10	is	be	VERB
hjic-943	223	11	no	no	DET
hjic-943	223	12	integration	integration	NOUN
hjic-943	223	13	for	for	ADP
hjic-943	223	14	variable	variable	ADJ
hjic-943	223	15	u	u	NOUN
hjic-943	223	16	in	in	ADP
hjic-943	223	17	the	the	DET
hjic-943	223	18	modified	modify	VERB
hjic-943	223	19	model	model	NOUN
hjic-943	223	20	,	,	PUNCT
hjic-943	223	21	so	so	SCONJ
hjic-943	223	22	it	it	PRON
hjic-943	223	23	is	be	AUX
hjic-943	223	24	not	not	PART
hjic-943	223	25	necessary	necessary	ADJ
hjic-943	223	26	to	to	PART
hjic-943	223	27	give	give	VERB
hjic-943	223	28	initial	initial	ADJ
hjic-943	223	29	value	value	NOUN
hjic-943	223	30	for	for	ADP
hjic-943	223	31	the	the	DET
hjic-943	223	32	variable	variable	NOUN
hjic-943	223	33	u.	u.	VERB
hjic-943	223	34	the	the	DET
hjic-943	223	35	representation	representation	NOUN
hjic-943	223	36	graph	graph	NOUN
hjic-943	223	37	of	of	ADP
hjic-943	223	38	the	the	DET
hjic-943	223	39	modified	modify	VERB
hjic-943	223	40	model	model	NOUN
hjic-943	223	41	can	can	AUX
hjic-943	223	42	be	be	AUX
hjic-943	223	43	seen	see	VERB
hjic-943	223	44	in	in	ADP
hjic-943	223	45	fig.6a	fig.6a	PROPN
hjic-943	223	46	.	.	PUNCT
hjic-943	224	1	the	the	DET
hjic-943	224	2	static	static	ADJ
hjic-943	224	3	graph	graph	NOUN
hjic-943	224	4	at	at	ADP
hjic-943	224	5	time	time	NOUN
hjic-943	224	6	step	step	NOUN
hjic-943	224	7	t+	t+	NOUN
hjic-943	224	8	1	1	NUM
hjic-943	224	9	shows	show	VERB
hjic-943	224	10	vertices	vertex	NOUN
hjic-943	224	11	belonging	belong	VERB
hjic-943	224	12	to	to	ADP
hjic-943	224	13	variables	variable	NOUN
hjic-943	224	14	only	only	ADV
hjic-943	224	15	,	,	PUNCT
hjic-943	224	16	which	which	PRON
hjic-943	224	17	are	be	AUX
hjic-943	224	18	necessary	necessary	ADJ
hjic-943	224	19	to	to	PART
hjic-943	224	20	calculate	calculate	VERB
hjic-943	224	21	q	q	NOUN
hjic-943	224	22	in	in	ADP
hjic-943	224	23	time	time	NOUN
hjic-943	224	24	step	step	NOUN
hjic-943	224	25	t.	t.	PROPN
hjic-943	224	26	the	the	DET
hjic-943	224	27	reduced	reduce	VERB
hjic-943	224	28	graph	graph	NOUN
hjic-943	224	29	is	be	AUX
hjic-943	224	30	shown	show	VERB
hjic-943	224	31	infig.6b	infig.6b	PROPN
hjic-943	224	32	.	.	PUNCT
hjic-943	225	1	it	it	PRON
hjic-943	225	2	can	can	AUX
hjic-943	225	3	be	be	AUX
hjic-943	225	4	seen	see	VERB
hjic-943	225	5	that	that	SCONJ
hjic-943	225	6	there	there	PRON
hjic-943	225	7	exists	exist	VERB
hjic-943	225	8	menger	menger	NOUN
hjic-943	225	9	~	~	NOUN
hjic-943	225	10	type	type	NOUN
hjic-943	225	11	complete	complete	ADJ
hjic-943	225	12	linking	linking	NOUN
hjic-943	225	13	on	on	ADP
hjic-943	225	14	the	the	DET
hjic-943	225	15	reduced	reduce	VERB
hjic-943	225	16	graph	graph	NOUN
hjic-943	225	17	,	,	PUNCT
hjic-943	225	18	so	so	CCONJ
hjic-943	225	19	the	the	DET
hjic-943	225	20	modified	modify	VERB
hjic-943	225	21	model	model	NOUN
hjic-943	225	22	is	be	AUX
hjic-943	225	23	conditionally	conditionally	ADV
hjic-943	225	24	structurally	structurally	ADV
hjic-943	225	25	solvable	solvable	ADJ
hjic-943	225	26	.	.	PUNCT
hjic-943	226	1	inspired	inspire	VERB
hjic-943	226	2	by	by	ADP
hjic-943	226	3	the	the	DET
hjic-943	226	4	above	above	ADJ
hjic-943	226	5	example	example	NOUN
hjic-943	226	6	we	we	PRON
hjic-943	226	7	generalized	generalize	VERB
hjic-943	226	8	the	the	DET
hjic-943	226	9	idea	idea	NOUN
hjic-943	226	10	of	of	ADP
hjic-943	226	11	using	use	VERB
hjic-943	226	12	the	the	DET
hjic-943	226	13	"	"	PUNCT
hjic-943	226	14	reverse	reverse	ADJ
hjic-943	226	15	information	information	NOUN
hjic-943	226	16	flow	flow	NOUN
hjic-943	226	17	"	"	PUNCT
hjic-943	226	18	for	for	ADP
hjic-943	226	19	computations	computation	NOUN
hjic-943	226	20	for	for	ADP
hjic-943	226	21	a	a	DET
hjic-943	226	22	wide	wide	ADJ
hjic-943	226	23	class	class	NOUN
hjic-943	226	24	of	of	ADP
hjic-943	226	25	semi	semi	ADJ
hjic-943	226	26	-	-	ADJ
hjic-943	226	27	explicit	explicit	ADJ
hjic-943	226	28	dae	dae	NOUN
hjic-943	226	29	systems	system	NOUN
hjic-943	226	30	and	and	CCONJ
hjic-943	226	31	formulated	formulate	VERB
hjic-943	226	32	a	a	DET
hjic-943	226	33	general	general	ADJ
hjic-943	226	34	index	index	NOUN
hjic-943	226	35	reduction	reduction	NOUN
hjic-943	226	36	algorithm	algorithm	NOUN
hjic-943	226	37	[	[	X
hjic-943	226	38	7	7	NUM
hjic-943	226	39	]	]	PUNCT
hjic-943	226	40	.	.	PUNCT
hjic-943	227	1	the	the	DET
hjic-943	227	2	effect	effect	NOUN
hjic-943	227	3	of	of	ADP
hjic-943	227	4	steady	steady	ADJ
hjic-943	227	5	state	state	NOUN
hjic-943	227	6	assumption	assumption	NOUN
hjic-943	227	7	models	model	NOUN
hjic-943	227	8	of	of	ADP
hjic-943	227	9	complex	complex	ADJ
hjic-943	227	10	dynamic	dynamic	ADJ
hjic-943	227	11	systems	system	NOUN
hjic-943	227	12	are	be	AUX
hjic-943	227	13	often	often	ADV
hjic-943	227	14	large­	large­	ADV
hjic-943	227	15	sized	sized	ADJ
hjic-943	227	16	and	and	CCONJ
hjic-943	227	17	complicated	complicated	ADJ
hjic-943	227	18	.	.	PUNCT
hjic-943	228	1	in	in	ADP
hjic-943	228	2	order	order	NOUN
hjic-943	228	3	to	to	PART
hjic-943	228	4	obtain	obtain	VERB
hjic-943	228	5	process	process	NOUN
hjic-943	228	6	models	model	NOUN
hjic-943	228	7	of	of	ADP
hjic-943	228	8	a	a	DET
hjic-943	228	9	reasonable	reasonable	ADJ
hjic-943	228	10	size	size	NOUN
hjic-943	228	11	we	we	PRON
hjic-943	228	12	most	most	ADV
hjic-943	228	13	often	often	ADV
hjic-943	228	14	use	use	VERB
hjic-943	228	15	model	model	NOUN
hjic-943	228	16	simplification	simplification	NOUN
hjic-943	228	17	.	.	PUNCT
hjic-943	229	1	the	the	DET
hjic-943	229	2	most	most	ADV
hjic-943	229	3	frequently	frequently	ADV
hjic-943	229	4	applied	apply	VERB
hjic-943	229	5	model	model	NOUN
hjic-943	229	6	simplification	simplification	NOUN
hjic-943	229	7	assumption	assumption	NOUN
hjic-943	229	8	originates	originate	NOUN
hjic-943	229	9	~om	~om	VERB
hjic-943	229	10	the	the	DET
hjic-943	229	11	st	st	PROPN
hjic-943	229	12	~	~	PROPN
hjic-943	229	13	a	a	DET
hjic-943	229	14	~	~	PUNCT
hjic-943	229	15	y	y	PROPN
hjic-943	229	16	state	state	NOUN
hjic-943	229	17	circumstances	circumstance	NOUN
hjic-943	229	18	valid	valid	ADJ
hjic-943	229	19	for	for	ADP
hjic-943	229	20	a	a	DET
hjic-943	229	21	state	state	NOUN
hjic-943	229	22	vanable	vanable	NOUN
hjic-943	229	23	.	.	PUNCT
hjic-943	230	1	our	our	PRON
hjic-943	230	2	a1	a1	NOUN
hjic-943	230	3	m	m	VERB
hjic-943	230	4	is	be	AUX
hjic-943	230	5	to	to	PART
hjic-943	230	6	investigate	investigate	VERB
hjic-943	230	7	how	how	SCONJ
hjic-943	230	8	the	the	DET
hjic-943	230	9	effect	effect	NOUN
hjic-943	230	10	of	of	ADP
hjic-943	230	11	steady	steady	ADJ
hjic-943	230	12	state	state	NOUN
hjic-943	230	13	assumption	assumption	NOUN
hjic-943	230	14	can	can	AUX
hjic-943	230	15	be	be	AUX
hjic-943	230	16	described	describe	VERB
hjic-943	230	17	on	on	ADP
hjic-943	230	18	the	the	DET
hjic-943	230	19	representation	representation	NOUN
hjic-943	230	20	graph	graph	NOUN
hjic-943	230	21	of	of	ADP
hjic-943	230	22	process	process	NOUN
hjic-943	230	23	models	model	NOUN
hjic-943	230	24	and	and	CCONJ
hjic-943	230	25	what	what	PRON
hjic-943	230	26	is	be	AUX
hjic-943	230	27	the	the	DET
hjic-943	230	28	effect	effect	NOUN
hjic-943	230	29	of	of	ADP
hjic-943	230	30	this	this	DET
hjic-943	230	31	assumption	assumption	NOUN
hjic-943	230	32	on	on	ADP
hjic-943	230	33	the	the	DET
hjic-943	230	34	68	68	NUM
hjic-943	230	35	structural	structural	ADJ
hjic-943	230	36	solvability	solvability	NOUN
hjic-943	230	37	,	,	PUNCT
hjic-943	230	38	model	model	NOUN
hjic-943	230	39	specification	specification	NOUN
hjic-943	230	40	and	and	CCONJ
hjic-943	230	41	differential	differential	ADJ
hjic-943	230	42	index	index	NOUN
hjic-943	230	43	.	.	PUNCT
hjic-943	231	1	steady	steady	ADJ
hjic-943	231	2	state	state	NOUN
hjic-943	231	3	assumption	assumption	NOUN
hjic-943	231	4	applied	apply	VERB
hjic-943	231	5	for	for	ADP
hjic-943	231	6	models	model	NOUN
hjic-943	231	7	with	with	ADP
hjic-943	231	8	differential	differential	ADJ
hjic-943	231	9	index	index	NOUN
hjic-943	231	10	1	1	NUM
hjic-943	231	11	consider	consider	VERB
hjic-943	231	12	a	a	DET
hjic-943	231	13	dynamic	dynamic	ADJ
hjic-943	231	14	process	process	NOUN
hjic-943	231	15	model	model	NOUN
hjic-943	231	16	described	describe	VERB
hjic-943	231	17	by	by	ADP
hjic-943	231	18	a	a	DET
hjic-943	231	19	semi­	semi­	ADJ
hjic-943	231	20	explicit	explicit	ADJ
hjic-943	231	21	dab	dab	NOUN
hjic-943	231	22	-	-	PUNCT
hjic-943	231	23	system	system	NOUN
hjic-943	231	24	with	with	ADP
hjic-943	231	25	differential	differential	ADJ
hjic-943	231	26	index	index	NOUN
hjic-943	231	27	1	1	NUM
hjic-943	231	28	.	.	PUNCT
hjic-943	232	1	a	a	DET
hjic-943	232	2	state	state	NOUN
hjic-943	232	3	variable	variable	NOUN
hjic-943	232	4	of	of	ADP
hjic-943	232	5	this	this	DET
hjic-943	232	6	model	model	NOUN
hjic-943	232	7	can	can	AUX
hjic-943	232	8	be	be	AUX
hjic-943	232	9	considered	consider	VERB
hjic-943	232	10	being	be	AUX
hjic-943	232	11	in	in	ADP
hjic-943	232	12	steady	steady	ADJ
hjic-943	232	13	state	state	NOUN
hjic-943	232	14	if	if	SCONJ
hjic-943	232	15	its	its	PRON
hjic-943	232	16	change	change	NOUN
hjic-943	232	17	in	in	ADP
hjic-943	232	18	time	time	NOUN
hjic-943	232	19	is	be	AUX
hjic-943	232	20	approximately	approximately	ADV
hjic-943	232	21	equal	equal	ADJ
hjic-943	232	22	to	to	ADP
hjic-943	232	23	0	0	NUM
hjic-943	232	24	,	,	PUNCT
hjic-943	232	25	compared	compare	VERB
hjic-943	232	26	to	to	ADP
hjic-943	232	27	the	the	DET
hjic-943	232	28	other	other	ADJ
hjic-943	232	29	terms	term	NOUN
hjic-943	232	30	of	of	ADP
hjic-943	232	31	the	the	DET
hjic-943	232	32	differential	differential	ADJ
hjic-943	232	33	equation	equation	NOUN
hjic-943	232	34	:	:	PUNCT
hjic-943	232	35	,	,	PUNCT
hjic-943	232	36	tfx	tfx	PROPN
hjic-943	232	37	x	x	SYM
hjic-943	232	38	=	=	NOUN
hjic-943	232	39	-:=::0	-:=::0	ADJ
hjic-943	232	40	dt	dt	X
hjic-943	232	41	(	(	PUNCT
hjic-943	232	42	50	50	NUM
hjic-943	232	43	)	)	PUNCT
hjic-943	232	44	this	this	DET
hjic-943	232	45	fact	fact	NOUN
hjic-943	232	46	can	can	AUX
hjic-943	232	47	be	be	AUX
hjic-943	232	48	treated	treat	VERB
hjic-943	232	49	on	on	ADP
hjic-943	232	50	the	the	DET
hjic-943	232	51	representation	representation	NOUN
hjic-943	232	52	graph	graph	NOUN
hjic-943	232	53	in	in	ADP
hjic-943	232	54	such	such	DET
hjic-943	232	55	a	a	DET
hjic-943	232	56	simple	simple	ADJ
hjic-943	232	57	way	way	NOUN
hjic-943	232	58	,	,	PUNCT
hjic-943	232	59	that	that	SCONJ
hjic-943	232	60	the	the	DET
hjic-943	232	61	assignment	assignment	NOUN
hjic-943	232	62	of	of	ADP
hjic-943	232	63	the	the	DET
hjic-943	232	64	derivative	derivative	ADJ
hjic-943	232	65	variable	variable	NOUN
hjic-943	232	66	x	x	SYM
hjic-943	232	67	1	1	NUM
hjic-943	232	68	becomes	become	VERB
hjic-943	232	69	type	type	NOUN
hjic-943	232	70	<	<	X
hjic-943	232	71	g	g	PROPN
hjic-943	232	72	>	>	X
hjic-943	232	73	,	,	PUNCT
hjic-943	232	74	because	because	SCONJ
hjic-943	232	75	the	the	DET
hjic-943	232	76	value	value	NOUN
hjic-943	232	77	of	of	ADP
hjic-943	232	78	x	x	NOUN
hjic-943	232	79	'	'	PUNCT
hjic-943	232	80	is	be	AUX
hjic-943	232	81	equal	equal	ADJ
hjic-943	232	82	to	to	ADP
hjic-943	232	83	zero	zero	NUM
hjic-943	232	84	.	.	PUNCT
hjic-943	233	1	the	the	DET
hjic-943	233	2	effect	effect	NOUN
hjic-943	233	3	of	of	ADP
hjic-943	233	4	this	this	DET
hjic-943	233	5	modification	modification	NOUN
hjic-943	233	6	to	to	ADP
hjic-943	233	7	the	the	DET
hjic-943	233	8	structural	structural	ADJ
hjic-943	233	9	solvability	solvability	NOUN
hjic-943	233	10	can	can	AUX
hjic-943	233	11	be	be	AUX
hjic-943	233	12	summarized	summarize	VERB
hjic-943	233	13	as	as	SCONJ
hjic-943	233	14	follows	follow	VERB
hjic-943	233	15	:	:	PUNCT
hjic-943	233	16	proposition	proposition	NOUN
hjic-943	233	17	1	1	NUM
hjic-943	233	18	:	:	PUNCT
hjic-943	233	19	consider	consider	VERB
hjic-943	233	20	a	a	DET
hjic-943	233	21	dynamic	dynamic	ADJ
hjic-943	233	22	process	process	NOUN
hjic-943	233	23	model	model	NOUN
hjic-943	233	24	described	describe	VERB
hjic-943	233	25	by	by	ADP
hjic-943	233	26	a	a	DET
hjic-943	233	27	semi	semi	ADJ
hjic-943	233	28	-	-	ADJ
hjic-943	233	29	explicit	explicit	ADJ
hjic-943	233	30	dae	dae	NOUN
hjic-943	233	31	system	system	NOUN
hjic-943	233	32	in	in	ADP
hjic-943	233	33	standard	standard	ADJ
hjic-943	233	34	form	form	NOUN
hjic-943	233	35	.	.	PUNCT
hjic-943	234	1	let	let	VERB
hjic-943	234	2	the	the	DET
hjic-943	234	3	differential	differential	ADJ
hjic-943	234	4	index	index	NOUN
hjic-943	234	5	of	of	ADP
hjic-943	234	6	this	this	DET
hjic-943	234	7	model	model	NOUN
hjic-943	234	8	be	be	VERB
hjic-943	234	9	1	1	NUM
hjic-943	234	10	.	.	PUNCT
hjic-943	234	11	assume	assume	VERB
hjic-943	234	12	that	that	SCONJ
hjic-943	234	13	the	the	DET
hjic-943	234	14	generality	generality	NOUN
hjic-943	234	15	assumption	assumption	NOUN
hjic-943	234	16	ga	ga	PROPN
hjic-943	234	17	is	be	AUX
hjic-943	234	18	true	true	ADJ
hjic-943	234	19	.	.	PUNCT
hjic-943	235	1	assume	assume	VERB
hjic-943	235	2	that	that	SCONJ
hjic-943	235	3	the	the	DET
hjic-943	235	4	size	size	NOUN
hjic-943	235	5	of	of	ADP
hjic-943	235	6	menger	menger	NOUN
hjic-943	235	7	-	-	PUNCT
hjic-943	235	8	type	type	NOUN
hjic-943	235	9	complete	complete	ADJ
hjic-943	235	10	linking	linking	NOUN
hjic-943	235	11	on	on	ADP
hjic-943	235	12	the	the	DET
hjic-943	235	13	static	static	ADJ
hjic-943	235	14	graphs	graph	NOUN
hjic-943	235	15	of	of	ADP
hjic-943	235	16	the	the	DET
hjic-943	235	17	dynamic	dynamic	ADJ
hjic-943	235	18	representation	representation	NOUN
hjic-943	235	19	graph	graph	NOUN
hjic-943	235	20	of	of	ADP
hjic-943	235	21	the	the	DET
hjic-943	235	22	model	model	NOUN
hjic-943	235	23	is	be	AUX
hjic-943	235	24	equal	equal	ADJ
hjic-943	235	25	to	to	ADP
hjic-943	235	26	k.	k.	PROPN
hjic-943	235	27	assume	assume	PROPN
hjic-943	235	28	,	,	PUNCT
hjic-943	235	29	that	that	SCONJ
hjic-943	235	30	the	the	DET
hjic-943	235	31	state	state	NOUN
hjic-943	235	32	variable	variable	NOUN
hjic-943	235	33	$	$	SYM
hjic-943	235	34	x$	x$	ADV
hjic-943	235	35	is	be	AUX
hjic-943	235	36	in	in	ADP
hjic-943	235	37	steady	steady	ADJ
hjic-943	235	38	state	state	NOUN
hjic-943	235	39	.	.	PUNCT
hjic-943	236	1	let	let	VERB
hjic-943	236	2	us	we	PRON
hjic-943	236	3	modify	modify	VERB
hjic-943	236	4	the	the	DET
hjic-943	236	5	assignment	assignment	NOUN
hjic-943	236	6	of	of	ADP
hjic-943	236	7	the	the	DET
hjic-943	236	8	vertex	vertex	NOUN
hjic-943	236	9	of	of	ADP
hjic-943	236	10	the	the	DET
hjic-943	236	11	derivative	derivative	ADJ
hjic-943	236	12	variable	variable	NOUN
hjic-943	236	13	x	x	NOUN
hjic-943	236	14	'	'	PUNCT
hjic-943	236	15	to	to	PART
hjic-943	236	16	type	type	VERB
hjic-943	236	17	<	<	X
hjic-943	236	18	g	g	PROPN
hjic-943	236	19	>	>	X
hjic-943	236	20	.	.	PUNCT
hjic-943	237	1	then	then	ADV
hjic-943	237	2	1	1	X
hjic-943	237	3	.	.	PUNCT
hjic-943	238	1	the	the	DET
hjic-943	238	2	static	static	ADJ
hjic-943	238	3	graphs	graph	NOUN
hjic-943	238	4	become	become	VERB
hjic-943	238	5	overspecified	overspecified	ADJ
hjic-943	238	6	at	at	ADP
hjic-943	238	7	any	any	DET
hjic-943	238	8	time	time	NOUN
hjic-943	238	9	step	step	NOUN
hjic-943	238	10	t	t	PROPN
hjic-943	238	11	,	,	PUNCT
hjic-943	238	12	hence	hence	ADV
hjic-943	238	13	there	there	PRON
hjic-943	238	14	are	be	VERB
hjic-943	238	15	no	no	DET
hjic-943	238	16	menger	menger	NOUN
hjic-943	238	17	-	-	PUNCT
hjic-943	238	18	type	type	NOUN
hjic-943	238	19	complete	complete	ADJ
hjic-943	238	20	linking	linking	NOUN
hjic-943	238	21	on	on	ADP
hjic-943	238	22	them	they	PRON
hjic-943	238	23	,	,	PUNCT
hjic-943	238	24	therefore	therefore	ADV
hjic-943	238	25	the	the	DET
hjic-943	238	26	model	model	NOUN
hjic-943	238	27	is	be	AUX
hjic-943	238	28	not	not	PART
hjic-943	238	29	structurally	structurally	ADV
hjic-943	238	30	solvable	solvable	ADJ
hjic-943	238	31	.	.	PUNCT
hjic-943	239	1	2	2	X
hjic-943	239	2	.	.	X
hjic-943	239	3	modify	modify	VERB
hjic-943	239	4	the	the	DET
hjic-943	239	5	model	model	NOUN
hjic-943	239	6	specification	specification	NOUN
hjic-943	239	7	as	as	SCONJ
hjic-943	239	8	follows	follow	VERB
hjic-943	239	9	.	.	PUNCT
hjic-943	240	1	consider	consider	VERB
hjic-943	240	2	that	that	SCONJ
hjic-943	240	3	there	there	PRON
hjic-943	240	4	exists	exist	VERB
hjic-943	240	5	a	a	DET
hjic-943	240	6	variable	variable	NOUN
hjic-943	240	7	xi	xi	X
hjic-943	240	8	on	on	ADP
hjic-943	240	9	the	the	DET
hjic-943	240	10	static	static	ADJ
hjic-943	240	11	graph	graph	NOUN
hjic-943	240	12	which	which	PRON
hjic-943	240	13	is	be	AUX
hjic-943	240	14	labelled	label	VERB
hjic-943	240	15	by	by	ADP
hjic-943	240	16	<	<	X
hjic-943	240	17	s	s	X
hjic-943	240	18	>	>	X
hjic-943	240	19	or	or	CCONJ
hjic-943	240	20	<	<	X
hjic-943	240	21	s	s	X
hjic-943	240	22	*	*	PUNCT
hjic-943	240	23	and	and	CCONJ
hjic-943	240	24	there	there	PRON
hjic-943	240	25	is	be	VERB
hjic-943	240	26	a	a	DET
hjic-943	240	27	directed	direct	VERB
hjic-943	240	28	path	path	NOUN
hjic-943	240	29	from	from	ADP
hjic-943	240	30	xi	xi	PROPN
hjic-943	240	31	into	into	ADP
hjic-943	240	32	x	x	PRON
hjic-943	240	33	,	,	PUNCT
hjic-943	240	34	which	which	PRON
hjic-943	240	35	is	be	AUX
hjic-943	240	36	vertex	vertex	NOUN
hjic-943	240	37	-	-	PUNCT
hjic-943	240	38	disjoint	disjoint	NOUN
hjic-943	240	39	to	to	ADP
hjic-943	240	40	paths	path	NOUN
hjic-943	240	41	of	of	ADP
hjic-943	240	42	a	a	DET
hjic-943	240	43	menger	menger	NOUN
hjic-943	240	44	-	-	PUNCT
hjic-943	240	45	type	type	NOUN
hjic-943	240	46	complete	complete	ADJ
hjic-943	240	47	linking	linking	NOUN
hjic-943	240	48	on	on	ADP
hjic-943	240	49	the	the	DET
hjic-943	240	50	original	original	ADJ
hjic-943	240	51	graph	graph	NOUN
hjic-943	240	52	.	.	PUNCT
hjic-943	241	1	drop	drop	VERB
hjic-943	241	2	the	the	DET
hjic-943	241	3	label	label	NOUN
hjic-943	241	4	<	<	X
hjic-943	241	5	s	s	X
hjic-943	241	6	>	>	X
hjic-943	241	7	or	or	CCONJ
hjic-943	241	8	<	<	X
hjic-943	241	9	s	s	X
hjic-943	241	10	*	*	X
hjic-943	241	11	of	of	ADP
hjic-943	241	12	variable	variable	NOUN
hjic-943	241	13	xj	xj	NOUN
hjic-943	241	14	·	·	PUNCT
hjic-943	241	15	after	after	ADP
hjic-943	241	16	this	this	PRON
hjic-943	241	17	:	:	PUNCT
hjic-943	241	18	there	there	PRON
hjic-943	241	19	is	be	VERB
hjic-943	241	20	a	a	DET
hjic-943	241	21	menger	menger	NOUN
hjic-943	241	22	-	-	PUNCT
hjic-943	241	23	type	type	NOUN
hjic-943	241	24	complete	complete	ADJ
hjic-943	241	25	linking	linking	NOUN
hjic-943	241	26	on	on	ADP
hjic-943	241	27	static	static	ADJ
hjic-943	241	28	graphs	graph	NOUN
hjic-943	241	29	at	at	ADP
hjic-943	241	30	any	any	DET
hjic-943	241	31	time	time	NOUN
hjic-943	241	32	step	step	NOUN
hjic-943	241	33	t.	t.	PROPN
hjic-943	242	1	so	so	ADV
hjic-943	242	2	the	the	DET
hjic-943	242	3	model	model	NOUN
hjic-943	242	4	is	be	AUX
hjic-943	242	5	structurally	structurally	ADV
hjic-943	242	6	solvable	solvable	ADJ
hjic-943	242	7	.	.	PUNCT
hjic-943	243	1	the	the	DET
hjic-943	243	2	size	size	NOUN
hjic-943	243	3	of	of	ADP
hjic-943	243	4	the	the	DET
hjic-943	243	5	menger­	menger­	NOUN
hjic-943	243	6	type	type	NOUN
hjic-943	243	7	complete	complete	ADJ
hjic-943	243	8	linking	linking	NOUN
hjic-943	243	9	is	be	AUX
hjic-943	243	10	equal	equal	ADJ
hjic-943	243	11	to	to	ADP
hjic-943	243	12	k+	k+	X
hjic-943	243	13	1	1	X
hjic-943	243	14	.	.	X
hjic-943	244	1	proof	proof	NOUN
hjic-943	244	2	:	:	PUNCT
hjic-943	244	3	let	let	VERB
hjic-943	244	4	g	g	NOUN
hjic-943	244	5	be	be	AUX
hjic-943	244	6	the	the	DET
hjic-943	244	7	static	static	ADJ
hjic-943	244	8	graph	graph	NOUN
hjic-943	244	9	of	of	ADP
hjic-943	244	10	the	the	DET
hjic-943	244	11	original	original	ADJ
hjic-943	244	12	dynamic	dynamic	ADJ
hjic-943	244	13	model	model	NOUN
hjic-943	244	14	at	at	ADP
hjic-943	244	15	time	time	NOUN
hjic-943	244	16	step	step	NOUN
hjic-943	244	17	t	t	PROPN
hjic-943	244	18	and	and	CCONJ
hjic-943	244	19	let	let	VERB
hjic-943	244	20	g	g	PRON
hjic-943	244	21	'	'	PUNCT
hjic-943	244	22	be	be	AUX
hjic-943	244	23	the	the	DET
hjic-943	244	24	modified	modify	VERB
hjic-943	244	25	static	static	ADJ
hjic-943	244	26	graph	graph	NOUN
hjic-943	244	27	.	.	PUNCT
hjic-943	245	1	l.	l.	PROPN
hjic-943	245	2	there	there	PRON
hjic-943	245	3	is	be	VERB
hjic-943	245	4	a	a	DET
hjic-943	245	5	menger	menger	NOUN
hjic-943	245	6	-	-	PUNCT
hjic-943	245	7	type	type	NOUN
hjic-943	245	8	complete	complete	ADJ
hjic-943	245	9	linking	linking	NOUN
hjic-943	245	10	on	on	ADP
hjic-943	245	11	the	the	DET
hjic-943	245	12	original	original	ADJ
hjic-943	245	13	static	static	ADJ
hjic-943	245	14	graph	graph	NOUN
hjic-943	245	15	g	g	NOUN
hjic-943	245	16	,	,	PUNCT
hjic-943	245	17	hence	hence	ADV
hjic-943	245	18	the	the	DET
hjic-943	245	19	elements	element	NOUN
hjic-943	245	20	of	of	ADP
hjic-943	245	21	variable	variable	ADJ
hjic-943	245	22	sets	set	NOUN
hjic-943	245	23	x	x	PUNCT
hjic-943	245	24	and	and	CCONJ
hjic-943	245	25	y	y	PROPN
hjic-943	245	26	are	be	AUX
hjic-943	245	27	equal	equal	ADJ
hjic-943	245	28	to	to	ADP
hjic-943	245	29	each	each	DET
hjic-943	245	30	other	other	ADJ
hjic-943	245	31	:	:	PUNCT
hjic-943	245	32	jx1	jx1	NOUN
hjic-943	245	33	=	=	SYM
hjic-943	245	34	jyi	jyi	PROPN
hjic-943	245	35	=	=	SYM
hjic-943	245	36	lc	lc	PROPN
hjic-943	245	37	.	.	PROPN
hjic-943	246	1	during	during	ADP
hjic-943	246	2	the	the	DET
hjic-943	246	3	modification	modification	NOUN
hjic-943	246	4	of	of	ADP
hjic-943	246	5	the	the	DET
hjic-943	246	6	assignment	assignment	NOUN
hjic-943	246	7	of	of	ADP
hjic-943	246	8	variable	variable	NOUN
hjic-943	246	9	x	x	NOUN
hjic-943	246	10	'	'	NUM
hjic-943	246	11	.	.	PUNCT
hjic-943	247	1	the	the	DET
hjic-943	247	2	number	number	NOUN
hjic-943	247	3	of	of	ADP
hjic-943	247	4	variables	variable	NOUN
hjic-943	247	5	labelled	label	VERB
hjic-943	247	6	by	by	ADP
hjic-943	247	7	type	type	NOUN
hjic-943	247	8	<	<	X
hjic-943	247	9	g	g	X
hjic-943	247	10	>	>	X
hjic-943	247	11	increases	increase	NOUN
hjic-943	247	12	.	.	PUNCT
hjic-943	248	1	hence	hence	ADV
hjic-943	248	2	g	g	NOUN
hjic-943	248	3	'	'	PUNCT
hjic-943	248	4	becomes	become	VERB
hjic-943	248	5	overspecified~	overspecified~	PROPN
hjic-943	249	1	so	so	ADV
hjic-943	249	2	there	there	PRON
hjic-943	249	3	is	be	VERB
hjic-943	249	4	no	no	DET
hjic-943	249	5	menger­	menger­	NOUN
hjic-943	249	6	type	type	NOUN
hjic-943	249	7	complete	complete	ADJ
hjic-943	249	8	linking	linking	NOUN
hjic-943	249	9	on	on	ADP
hjic-943	249	10	it	it	PRON
hjic-943	249	11	.	.	PUNCT
hjic-943	250	1	$	$	SYM
hjic-943	250	2	<	<	X
hjic-943	250	3	g	g	X
hjic-943	250	4	>	>	X
hjic-943	250	5	fo~	fo~	PROPN
hjic-943	250	6	·	·	PUNCT
hjic-943	250	7	.	.	PUNCT
hjic-943	250	8	·	·	PUNCT
hjic-943	250	9	.dm	.dm	PUNCT
hjic-943	251	1	<	<	X
hjic-943	251	2	g	g	X
hjic-943	251	3	>	>	X
hjic-943	251	4	.	.	PUNCT
hjic-943	252	1	du	du	PROPN
hjic-943	252	2	du	du	PROPN
hjic-943	252	3	tt---	tt---	PROPN
hjic-943	252	4	....	....	PUNCT
hjic-943	253	1	h~	h~	PROPN
hjic-943	253	2	_	_	PUNCT
hjic-943	254	1	_	_	PUNCT
hjic-943	255	1	_	_	PUNCT
hjic-943	256	1	_	_	PUNCT
hjic-943	256	2	,	,	PUNCT
hjic-943	256	3	,	,	PUNCT
hjic-943	256	4	..	..	PUNCT
hjic-943	256	5	<	<	X
hjic-943	256	6	~	~	PUNCT
hjic-943	256	7	>	>	X
hjic-943	256	8	a	a	DET
hjic-943	256	9	,	,	PUNCT
hjic-943	256	10	b	b	NOUN
hjic-943	256	11	,	,	PUNCT
hjic-943	256	12	u••-----·~-~~l---·-··~···-1	u••-----·~-~~l---·-··~···-1	PROPN
hjic-943	256	13	du	du	PROPN
hjic-943	256	14	~<g	~<g	PROPN
hjic-943	256	15	>	>	X
hjic-943	256	16	tl	tl	PROPN
hjic-943	257	1	_	_	PUNCT
hjic-943	258	1	_	_	PUNCT
hjic-943	259	1	_	_	PUNCT
hjic-943	259	2	.	.	PUNCT
hjic-943	260	1	,	,	PUNCT
hjic-943	260	2	.....	.....	PUNCT
hjic-943	261	1	_	_	PUNCT
hjic-943	261	2	_	_	PUNCT
hjic-943	261	3	~s	~s	PUNCT
hjic-943	262	1	h~	h~	PROPN
hjic-943	262	2	<	<	X
hjic-943	262	3	g	g	X
hjic-943	262	4	>	>	X
hjic-943	262	5	o-----------~:~	o-----------~:~	NOUN
hjic-943	262	6	c	c	NOUN
hjic-943	262	7	,	,	PUNCT
hjic-943	262	8	d	d	NOUN
hjic-943	262	9	,	,	PUNCT
hjic-943	262	10	fig.7	fig.7	ADJ
hjic-943	262	11	reduced	reduced	ADJ
hjic-943	262	12	graph	graph	NOUN
hjic-943	262	13	of	of	ADP
hjic-943	262	14	model	model	NOUN
hjic-943	262	15	in	in	ADP
hjic-943	262	16	example	example	NOUN
hjic-943	262	17	2	2	NUM
hjic-943	262	18	with	with	ADP
hjic-943	262	19	specification	specification	NOUN
hjic-943	263	1	i	i	PRON
hjic-943	263	2	;	;	PUNCT
hjic-943	263	3	a	a	PRON
hjic-943	263	4	,	,	PUNCT
hjic-943	263	5	assuming	assume	VERB
hjic-943	263	6	steady	steady	ADJ
hjic-943	263	7	state	state	NOUN
hjic-943	263	8	for	for	ADP
hjic-943	263	9	m	m	PROPN
hjic-943	263	10	(	(	PUNCT
hjic-943	263	11	mo	mo	PROPN
hjic-943	263	12	is	be	AUX
hjic-943	263	13	considered	consider	VERB
hjic-943	263	14	to	to	PART
hjic-943	263	15	be	be	AUX
hjic-943	263	16	unknown	unknown	ADJ
hjic-943	263	17	)	)	PUNCT
hjic-943	263	18	;	;	PUNCT
hjic-943	263	19	b	b	X
hjic-943	263	20	,	,	PUNCT
hjic-943	263	21	assuming	assume	VERB
hjic-943	263	22	steady	steady	ADJ
hjic-943	263	23	state	state	NOUN
hjic-943	263	24	form	form	NOUN
hjic-943	263	25	(	(	PUNCT
hjic-943	263	26	f	f	PROPN
hjic-943	263	27	is	be	AUX
hjic-943	263	28	considered	consider	VERB
hjic-943	263	29	to	to	PART
hjic-943	263	30	be	be	AUX
hjic-943	263	31	unknown	unknown	ADJ
hjic-943	263	32	)	)	PUNCT
hjic-943	263	33	;	;	PUNCT
hjic-943	263	34	c	c	X
hjic-943	263	35	,	,	PUNCT
hjic-943	263	36	assuming	assume	VERB
hjic-943	263	37	steady	steady	ADJ
hjic-943	263	38	state	state	NOUN
hjic-943	263	39	for	for	ADP
hjic-943	263	40	u	u	PROPN
hjic-943	263	41	(	(	PUNCT
hjic-943	263	42	u0	u0	ADJ
hjic-943	263	43	is	be	AUX
hjic-943	263	44	considered	consider	VERB
hjic-943	263	45	to	to	PART
hjic-943	263	46	be	be	AUX
hjic-943	263	47	unknown	unknown	ADJ
hjic-943	263	48	)	)	PUNCT
hjic-943	263	49	;	;	PUNCT
hjic-943	264	1	d	d	X
hjic-943	264	2	,	,	PUNCT
hjic-943	264	3	assuming	assume	VERB
hjic-943	264	4	steady	steady	ADJ
hjic-943	264	5	state	state	NOUN
hjic-943	264	6	for	for	ADP
hjic-943	264	7	u	u	PROPN
hjic-943	264	8	(	(	PUNCT
hjic-943	264	9	q	q	PROPN
hjic-943	264	10	is	be	AUX
hjic-943	264	11	considered	consider	VERB
hjic-943	264	12	to	to	PART
hjic-943	264	13	be	be	AUX
hjic-943	264	14	unknown	unknown	ADJ
hjic-943	264	15	)	)	PUNCT
hjic-943	264	16	2	2	NUM
hjic-943	264	17	.	.	X
hjic-943	264	18	changing	change	VERB
hjic-943	264	19	the	the	DET
hjic-943	264	20	model	model	NOUN
hjic-943	264	21	specification	specification	NOUN
hjic-943	264	22	the	the	DET
hjic-943	264	23	way	way	NOUN
hjic-943	264	24	described	describe	VERB
hjic-943	264	25	above	above	ADV
hjic-943	264	26	,	,	PUNCT
hjic-943	264	27	the	the	DET
hjic-943	264	28	following	follow	VERB
hjic-943	264	29	is	be	AUX
hjic-943	264	30	true	true	ADJ
hjic-943	264	31	on	on	ADP
hjic-943	264	32	the	the	DET
hjic-943	264	33	reduced	reduce	VERB
hjic-943	264	34	graph	graph	NOUN
hjic-943	264	35	of	of	ADP
hjic-943	264	36	g	g	NOUN
hjic-943	264	37	'	'	PUNCT
hjic-943	264	38	:	:	PUNCT
hjic-943	265	1	ix'i	ix'i	PROPN
hjic-943	265	2	=	=	SYM
hjic-943	265	3	iy'i	iy'i	PROPN
hjic-943	265	4	=	=	PUNCT
hjic-943	265	5	k+	k+	NOUN
hjic-943	265	6	1	1	NUM
hjic-943	265	7	and	and	CCONJ
hjic-943	265	8	there	there	PRON
hjic-943	265	9	is	be	VERB
hjic-943	265	10	a	a	DET
hjic-943	265	11	directed	direct	VERB
hjic-943	265	12	path	path	NOUN
hjic-943	265	13	from	from	ADP
hjic-943	265	14	xi	xi	NOUN
hjic-943	265	15	into	into	ADP
hjic-943	265	16	vertex	vertex	NOUN
hjic-943	265	17	x	x	NOUN
hjic-943	265	18	'	'	PUNCT
hjic-943	265	19	,	,	PUNCT
hjic-943	265	20	which	which	PRON
hjic-943	265	21	gives	give	VERB
hjic-943	265	22	a	a	DET
hjic-943	265	23	menger	menger	NOUN
hjic-943	265	24	-	-	PUNCT
hjic-943	265	25	type	type	NOUN
hjic-943	265	26	complete	complete	ADJ
hjic-943	265	27	linking	linking	NOUN
hjic-943	265	28	on	on	ADP
hjic-943	265	29	g	g	NOUN
hjic-943	265	30	'	'	PUNCT
hjic-943	265	31	with	with	ADP
hjic-943	265	32	a	a	DET
hjic-943	265	33	suitable	suitable	ADJ
hjic-943	265	34	menger	menger	NOUN
hjic-943	265	35	-	-	PUNCT
hjic-943	265	36	type	type	NOUN
hjic-943	265	37	complete	complete	ADJ
hjic-943	265	38	linking	linking	NOUN
hjic-943	265	39	on	on	ADP
hjic-943	265	40	the	the	DET
hjic-943	265	41	reduced	reduce	VERB
hjic-943	265	42	graph	graph	NOUN
hjic-943	265	43	of	of	ADP
hjic-943	265	44	g.	g.	PROPN
hjic-943	265	45	consequence	consequence	PROPN
hjic-943	265	46	:	:	PUNCT
hjic-943	265	47	changing	change	VERB
hjic-943	265	48	the	the	DET
hjic-943	265	49	variable	variable	ADJ
hjic-943	265	50	assignment	assignment	NOUN
hjic-943	265	51	(	(	PUNCT
hjic-943	265	52	and	and	CCONJ
hjic-943	265	53	the	the	DET
hjic-943	265	54	model	model	NOUN
hjic-943	265	55	specification	specification	NOUN
hjic-943	265	56	)	)	PUNCT
hjic-943	265	57	according	accord	VERB
hjic-943	265	58	to	to	ADP
hjic-943	265	59	proposition	proposition	NOUN
hjic-943	265	60	1	1	NUM
hjic-943	265	61	above	above	ADV
hjic-943	265	62	,	,	PUNCT
hjic-943	265	63	the	the	DET
hjic-943	265	64	differential	differential	ADJ
hjic-943	265	65	index	index	NOUN
hjic-943	265	66	of	of	ADP
hjic-943	265	67	the	the	DET
hjic-943	265	68	dynamic	dynamic	ADJ
hjic-943	265	69	model	model	NOUN
hjic-943	265	70	does	do	AUX
hjic-943	265	71	not	not	PART
hjic-943	265	72	change	change	VERB
hjic-943	265	73	.	.	PUNCT
hjic-943	266	1	example	example	NOUN
hjic-943	266	2	2	2	NUM
hjic-943	266	3	(	(	PUNCT
hjic-943	266	4	continued	continue	VERB
hjic-943	266	5	)	)	PUNCT
hjic-943	266	6	.	.	PUNCT
hjic-943	267	1	consider	consider	VERB
hjic-943	267	2	example	example	NOUN
hjic-943	267	3	2	2	NUM
hjic-943	267	4	with	with	ADP
hjic-943	267	5	specification	specification	NOUN
hjic-943	267	6	1	1	NUM
hjic-943	267	7	.	.	NOUN
hjic-943	267	8	1	1	NUM
hjic-943	267	9	.	.	X
hjic-943	267	10	assume	assume	VERB
hjic-943	267	11	,	,	PUNCT
hjic-943	267	12	that	that	SCONJ
hjic-943	267	13	the	the	DET
hjic-943	267	14	mass	mass	NOUN
hjic-943	267	15	in	in	ADP
hjic-943	267	16	the	the	DET
hjic-943	267	17	tank	tank	NOUN
hjic-943	267	18	is	be	AUX
hjic-943	267	19	in	in	ADP
hjic-943	267	20	steady	steady	ADJ
hjic-943	267	21	state	state	NOUN
hjic-943	267	22	,	,	PUNCT
hjic-943	267	23	that	that	ADV
hjic-943	267	24	is	is	ADV
hjic-943	267	25	.	.	PUNCT
hjic-943	268	1	(	(	PUNCT
hjic-943	268	2	51	51	NUM
hjic-943	268	3	)	)	PUNCT
hjic-943	268	4	according	accord	VERB
hjic-943	268	5	to	to	ADP
hjic-943	268	6	the	the	DET
hjic-943	268	7	above	above	NOUN
hjic-943	268	8	,	,	PUNCT
hjic-943	268	9	this	this	DET
hjic-943	268	10	assumption	assumption	NOUN
hjic-943	268	11	can	can	AUX
hjic-943	268	12	be	be	AUX
hjic-943	268	13	treated	treat	VERB
hjic-943	268	14	on	on	ADP
hjic-943	268	15	the	the	DET
hjic-943	268	16	representation	representation	NOUN
hjic-943	268	17	graph	graph	NOUN
hjic-943	268	18	by	by	ADP
hjic-943	268	19	modifying	modify	VERB
hjic-943	268	20	the	the	DET
hjic-943	268	21	assignment	assignment	NOUN
hjic-943	268	22	of	of	ADP
hjic-943	268	23	vertex	vertex	NOUN
hjic-943	268	24	m	m	NOUN
hjic-943	268	25	'	'	PUNCT
hjic-943	268	26	in	in	ADP
hjic-943	268	27	such	such	DET
hjic-943	268	28	a	a	DET
hjic-943	268	29	way	way	NOUN
hjic-943	268	30	that	that	PRON
hjic-943	268	31	it	it	PRON
hjic-943	268	32	is	be	AUX
hjic-943	268	33	labelled	label	VERB
hjic-943	268	34	by	by	ADP
hjic-943	268	35	type	type	NOUN
hjic-943	268	36	<	<	X
hjic-943	268	37	g	g	PROPN
hjic-943	268	38	>	>	X
hjic-943	268	39	.	.	PUNCT
hjic-943	269	1	after	after	ADP
hjic-943	269	2	this	this	PRON
hjic-943	269	3	,	,	PUNCT
hjic-943	269	4	all	all	DET
hjic-943	269	5	static	static	ADJ
hjic-943	269	6	graphs	graph	NOUN
hjic-943	269	7	become	become	VERB
hjic-943	269	8	overspecified	overspecified	ADJ
hjic-943	269	9	.	.	PUNCT
hjic-943	270	1	according	accord	VERB
hjic-943	270	2	to	to	ADP
hjic-943	270	3	fig.4a	fig.4a	PROPN
hjic-943	270	4	there	there	ADV
hjic-943	270	5	exist	exist	VERB
hjic-943	270	6	two	two	NUM
hjic-943	270	7	vertices	vertex	NOUN
hjic-943	270	8	(	(	PUNCT
hjic-943	270	9	m	m	X
hjic-943	270	10	and	and	CCONJ
hjic-943	270	11	f	f	X
hjic-943	270	12	)	)	PUNCT
hjic-943	270	13	on	on	ADP
hjic-943	270	14	the	the	DET
hjic-943	270	15	representati	representati	PROPN
hjic-943	270	16	~	~	PUNCT
hjic-943	270	17	n	n	NOUN
hjic-943	270	18	graph	graph	NOUN
hjic-943	270	19	which	which	PRON
hjic-943	270	20	are	be	AUX
hjic-943	270	21	labelled	label	VERB
hjic-943	270	22	by	by	ADP
hjic-943	270	23	type	type	NOUN
hjic-943	270	24	<	<	X
hjic-943	270	25	s	s	X
hjic-943	270	26	>	>	X
hjic-943	270	27	or	or	CCONJ
hjic-943	270	28	<	<	X
hjic-943	270	29	s	s	X
hjic-943	270	30	>	>	X
hjic-943	270	31	and	and	CCONJ
hjic-943	270	32	from	from	ADP
hjic-943	270	33	which	which	PRON
hjic-943	270	34	a	a	DET
hjic-943	270	35	directed	direct	VERB
hjic-943	270	36	path	path	NOUN
hjic-943	270	37	starts	start	VERB
hjic-943	270	38	into	into	ADP
hjic-943	270	39	vertex	vertex	NOUN
hjic-943	270	40	m	m	NOUN
hjic-943	270	41	'	'	NUM
hjic-943	270	42	.	.	PUNCT
hjic-943	271	1	both	both	PRON
hjic-943	271	2	of	of	ADP
hjic-943	271	3	these	these	DET
hjic-943	271	4	paths	path	NOUN
hjic-943	271	5	are	be	AUX
hjic-943	271	6	vertex	vertex	NOUN
hjic-943	271	7	-	-	PUNCT
hjic-943	271	8	disjoint	disjoint	NOUN
hjic-943	271	9	with	with	ADP
hjic-943	271	10	the	the	DET
hjic-943	271	11	menger	menger	NOUN
hjic-943	271	12	-	-	PUNCT
hjic-943	271	13	type	type	NOUN
hjic-943	271	14	complete	complete	ADJ
hjic-943	271	15	linking	linking	NOUN
hjic-943	271	16	of	of	ADP
hjic-943	271	17	the	the	DET
hjic-943	271	18	original	original	ADJ
hjic-943	271	19	reduced	reduce	VERB
hjic-943	271	20	graph	graph	NOUN
hjic-943	271	21	(	(	PUNCT
hjic-943	271	22	see	see	VERB
hjic-943	271	23	fig.4h	fig.4h	NOUN
hjic-943	271	24	)	)	PUNCT
hjic-943	271	25	.	.	PUNCT
hjic-943	272	1	hence	hence	ADV
hjic-943	272	2	there	there	PRON
hjic-943	272	3	are	be	VERB
hjic-943	272	4	two	two	NUM
hjic-943	272	5	possibilities	possibility	NOUN
hjic-943	272	6	to	to	PART
hjic-943	272	7	modify	modify	VERB
hjic-943	272	8	specification	specification	NOUN
hjic-943	272	9	according	accord	VERB
hjic-943	272	10	to	to	ADP
hjic-943	272	11	proposition	proposition	NOUN
hjic-943	272	12	1	1	NUM
hjic-943	272	13	.	.	PUNCT
hjic-943	272	14	either	either	CCONJ
hjic-943	272	15	the	the	DET
hjic-943	272	16	initial	initial	ADJ
hjic-943	272	17	value	value	NOUN
hjic-943	272	18	of	of	ADP
hjic-943	272	19	mass	mass	ADJ
hjic-943	272	20	m0	m0	NOUN
hjic-943	272	21	or	or	CCONJ
hjic-943	272	22	the	the	DET
hjic-943	272	23	inlet	inlet	ADJ
hjic-943	272	24	mass	mass	NOUN
hjic-943	272	25	flow	flow	NOUN
hjic-943	272	26	rate	rate	NOUN
hjic-943	272	27	f	f	PROPN
hjic-943	272	28	can	can	AUX
hjic-943	272	29	be	be	AUX
hjic-943	272	30	unknown	unknown	ADJ
hjic-943	272	31	,	,	PUNCT
hjic-943	272	32	so	so	CCONJ
hjic-943	272	33	the	the	DET
hjic-943	272	34	original	original	ADJ
hjic-943	272	35	label	label	NOUN
hjic-943	272	36	of	of	ADP
hjic-943	272	37	one	one	NUM
hjic-943	272	38	of	of	ADP
hjic-943	272	39	these	these	DET
hjic-943	272	40	vertices	vertex	NOUN
hjic-943	272	41	can	can	AUX
hjic-943	272	42	be	be	AUX
hjic-943	272	43	dropped	drop	VERB
hjic-943	272	44	on	on	ADP
hjic-943	272	45	the	the	DET
hjic-943	272	46	representation	representation	NOUN
hjic-943	272	47	graph	graph	NOUN
hjic-943	272	48	.	.	PUNCT
hjic-943	273	1	with	with	ADP
hjic-943	273	2	these	these	DET
hjic-943	273	3	modifications	modification	NOUN
hjic-943	273	4	the	the	DET
hjic-943	273	5	new	new	ADJ
hjic-943	273	6	reduced	reduce	VERB
hjic-943	273	7	graphs	graph	NOUN
hjic-943	273	8	can	can	AUX
hjic-943	273	9	be	be	AUX
hjic-943	273	10	seen	see	VERB
hjic-943	273	11	in	in	ADP
hjic-943	273	12	figs.7a	figs.7a	NOUN
hjic-943	273	13	and	and	CCONJ
hjic-943	273	14	lb	lb	NOUN
hjic-943	273	15	.	.	NOUN
hjic-943	274	1	b	b	X
hjic-943	274	2	,	,	PUNCT
hjic-943	274	3	fig.8	fig.8	PROPN
hjic-943	274	4	reduced	reduce	VERB
hjic-943	274	5	graph	graph	NOUN
hjic-943	274	6	of	of	ADP
hjic-943	274	7	model	model	NOUN
hjic-943	274	8	in	in	ADP
hjic-943	274	9	example	example	NOUN
hjic-943	274	10	2	2	NUM
hjic-943	274	11	with	with	ADP
hjic-943	274	12	specification	specification	NOUN
hjic-943	274	13	1	1	NUM
hjic-943	274	14	assuming	assume	VERB
hjic-943	274	15	steady	steady	ADJ
hjic-943	274	16	state	state	NOUN
hjic-943	274	17	for	for	ADP
hjic-943	274	18	m	m	PROPN
hjic-943	274	19	and	and	CCONJ
hjic-943	274	20	u	u	NOUN
hjic-943	274	21	;	;	PUNCT
hjic-943	274	22	a	a	PRON
hjic-943	274	23	,	,	PUNCT
hjic-943	274	24	m0	m0	NOUN
hjic-943	274	25	and	and	CCONJ
hjic-943	274	26	u0	u0	PROPN
hjic-943	274	27	are	be	AUX
hjic-943	274	28	considered	consider	VERB
hjic-943	274	29	to	to	PART
hjic-943	274	30	be	be	AUX
hjic-943	274	31	unknown	unknown	ADJ
hjic-943	274	32	;	;	PUNCT
hjic-943	274	33	b	b	X
hjic-943	274	34	,	,	PUNCT
hjic-943	274	35	f	f	PROPN
hjic-943	274	36	and	and	CCONJ
hjic-943	274	37	q	q	PROPN
hjic-943	274	38	are	be	AUX
hjic-943	274	39	considered	consider	VERB
hjic-943	274	40	to	to	PART
hjic-943	274	41	be	be	AUX
hjic-943	274	42	unknown	unknown	ADJ
hjic-943	274	43	in	in	ADP
hjic-943	274	44	both	both	DET
hjic-943	274	45	cases	case	NOUN
hjic-943	274	46	there	there	PRON
hjic-943	274	47	is	be	VERB
hjic-943	274	48	a	a	DET
hjic-943	274	49	menger	menger	NOUN
hjic-943	274	50	-	-	PUNCT
hjic-943	274	51	type	type	NOUN
hjic-943	274	52	complete	complete	ADJ
hjic-943	274	53	linking	linking	NOUN
hjic-943	274	54	on	on	ADP
hjic-943	274	55	the	the	DET
hjic-943	274	56	reduced	reduce	VERB
hjic-943	274	57	graph	graph	NOUN
hjic-943	274	58	,	,	PUNCT
hjic-943	274	59	so	so	SCONJ
hjic-943	274	60	the	the	DET
hjic-943	274	61	model	model	NOUN
hjic-943	274	62	is	be	AUX
hjic-943	274	63	conditionally	conditionally	ADV
hjic-943	274	64	structurally	structurally	ADV
hjic-943	274	65	solvable	solvable	ADJ
hjic-943	274	66	.	.	PUNCT
hjic-943	275	1	the	the	DET
hjic-943	275	2	size	size	NOUN
hjic-943	275	3	of	of	ADP
hjic-943	275	4	menger	menger	NOUN
hjic-943	275	5	-	-	PUNCT
hjic-943	275	6	type	type	NOUN
hjic-943	275	7	complete	complete	ADJ
hjic-943	275	8	linking	linking	NOUN
hjic-943	275	9	increases	increase	NOUN
hjic-943	275	10	from	from	ADP
hjic-943	275	11	1	1	NUM
hjic-943	275	12	to	to	ADP
hjic-943	275	13	2	2	NUM
hjic-943	275	14	.	.	NOUN
hjic-943	275	15	2	2	NUM
hjic-943	275	16	.	.	X
hjic-943	275	17	consider	consider	VERB
hjic-943	275	18	that	that	SCONJ
hjic-943	275	19	the	the	DET
hjic-943	275	20	internal	internal	ADJ
hjic-943	275	21	energy	energy	NOUN
hjic-943	275	22	of	of	ADP
hjic-943	275	23	liquid	liquid	NOUN
hjic-943	275	24	in	in	ADP
hjic-943	275	25	the	the	DET
hjic-943	275	26	tank	tank	NOUN
hjic-943	275	27	is	be	AUX
hjic-943	275	28	in	in	ADP
hjic-943	275	29	steady	steady	ADJ
hjic-943	275	30	state	state	NOUN
hjic-943	275	31	,	,	PUNCT
hjic-943	275	32	that	that	PRON
hjic-943	275	33	is	be	AUX
hjic-943	275	34	u	u	NOUN
hjic-943	275	35	·	·	PUNCT
hjic-943	275	36	~a	~a	PUNCT
hjic-943	275	37	(	(	PUNCT
hjic-943	275	38	52	52	NUM
hjic-943	275	39	)	)	PUNCT
hjic-943	275	40	let	let	VERB
hjic-943	275	41	the	the	DET
hjic-943	275	42	value	value	NOUN
hjic-943	275	43	of	of	ADP
hjic-943	275	44	the	the	DET
hjic-943	275	45	derivative	derivative	ADJ
hjic-943	275	46	variable	variable	ADJ
hjic-943	275	47	u	u	NOUN
hjic-943	275	48	'	'	PUNCT
hjic-943	275	49	be	be	VERB
hjic-943	275	50	equal	equal	ADJ
hjic-943	275	51	to	to	ADP
hjic-943	275	52	zero	zero	NUM
hjic-943	275	53	,	,	PUNCT
hjic-943	275	54	so	so	SCONJ
hjic-943	275	55	it	it	PRON
hjic-943	275	56	becomes	becomes	AUX
hjic-943	275	57	to	to	PART
hjic-943	275	58	be	be	AUX
hjic-943	275	59	labelled	label	VERB
hjic-943	275	60	by	by	ADP
hjic-943	275	61	type	type	NOUN
hjic-943	275	62	<	<	X
hjic-943	275	63	g	g	PROPN
hjic-943	275	64	>	>	X
hjic-943	275	65	.it	.it	PUNCT
hjic-943	275	66	can	can	AUX
hjic-943	275	67	be	be	AUX
hjic-943	275	68	seen	see	VERB
hjic-943	275	69	in	in	ADP
hjic-943	275	70	fig.4a	fig.4a	NOUN
hjic-943	275	71	that	that	SCONJ
hjic-943	275	72	there	there	PRON
hjic-943	275	73	are	be	VERB
hjic-943	275	74	six	six	NUM
hjic-943	275	75	vertices	vertex	NOUN
hjic-943	275	76	(	(	PUNCT
hjic-943	275	77	m	m	PROPN
hjic-943	275	78	,	,	PUNCT
hjic-943	275	79	f	f	PROPN
hjic-943	275	80	,	,	PUNCT
hjic-943	275	81	u	u	PROPN
hjic-943	275	82	,	,	PUNCT
hjic-943	275	83	tl	tl	PROPN
hjic-943	275	84	,	,	PUNCT
hjic-943	275	85	p	p	PROPN
hjic-943	275	86	f	f	PROPN
hjic-943	275	87	and	and	CCONJ
hjic-943	275	88	q	q	X
hjic-943	275	89	)	)	PUNCT
hjic-943	275	90	on	on	ADP
hjic-943	275	91	the	the	DET
hjic-943	275	92	static	static	ADJ
hjic-943	275	93	graph	graph	NOUN
hjic-943	275	94	which	which	PRON
hjic-943	275	95	are	be	AUX
hjic-943	275	96	labelled	label	VERB
hjic-943	275	97	by	by	ADP
hjic-943	275	98	<	<	X
hjic-943	275	99	s	s	X
hjic-943	275	100	>	>	X
hjic-943	275	101	or	or	CCONJ
hjic-943	275	102	<	<	X
hjic-943	275	103	s	s	X
hjic-943	275	104	*	*	X
hjic-943	275	105	>	>	X
hjic-943	275	106	and	and	CCONJ
hjic-943	275	107	from	from	ADP
hjic-943	275	108	which	which	PRON
hjic-943	275	109	a	a	DET
hjic-943	275	110	directed	direct	VERB
hjic-943	275	111	path	path	NOUN
hjic-943	275	112	starts	start	VERB
hjic-943	275	113	to	to	PART
hjic-943	275	114	vertex	vertex	VERB
hjic-943	275	115	u	u	NOUN
hjic-943	275	116	'	'	PUNCT
hjic-943	275	117	.	.	PUNCT
hjic-943	276	1	dropping	drop	VERB
hjic-943	276	2	the	the	DET
hjic-943	276	3	label	label	NOUN
hjic-943	276	4	<	<	X
hjic-943	276	5	s	s	X
hjic-943	276	6	>	>	X
hjic-943	276	7	or	or	CCONJ
hjic-943	276	8	<	<	X
hjic-943	276	9	s	s	PROPN
hjic-943	276	10	*	*	X
hjic-943	276	11	>	>	X
hjic-943	276	12	of	of	ADP
hjic-943	276	13	any	any	PRON
hjic-943	276	14	of	of	ADP
hjic-943	276	15	these	these	DET
hjic-943	276	16	vertices	vertex	NOUN
hjic-943	276	17	is	be	AUX
hjic-943	276	18	suitable	suitable	ADJ
hjic-943	276	19	to	to	PART
hjic-943	276	20	obtain	obtain	VERB
hjic-943	276	21	a	a	DET
hjic-943	276	22	conditionally	conditionally	ADV
hjic-943	276	23	structurally	structurally	ADV
hjic-943	276	24	solvable	solvable	ADJ
hjic-943	276	25	model	model	NOUN
hjic-943	276	26	.	.	PUNCT
hjic-943	277	1	figs.7c	figs.7c	PROPN
hjic-943	277	2	and	and	CCONJ
hjic-943	277	3	7d	7d	NUM
hjic-943	277	4	show	show	VERB
hjic-943	277	5	the	the	DET
hjic-943	277	6	reduced	reduce	VERB
hjic-943	277	7	graphs	graph	NOUN
hjic-943	277	8	of	of	ADP
hjic-943	277	9	the	the	DET
hjic-943	277	10	modified	modify	VERB
hjic-943	277	11	model	model	NOUN
hjic-943	277	12	.	.	PUNCT
hjic-943	278	1	in	in	ADP
hjic-943	278	2	the	the	DET
hjic-943	278	3	first	first	ADJ
hjic-943	278	4	case	case	NOUN
hjic-943	278	5	variable	variable	ADJ
hjic-943	278	6	u	u	NOUN
hjic-943	278	7	while	while	SCONJ
hjic-943	278	8	in	in	ADP
hjic-943	278	9	the	the	DET
hjic-943	278	10	other	other	ADJ
hjic-943	278	11	case	case	NOUN
hjic-943	278	12	variable	variable	NOUN
hjic-943	278	13	q	q	NOUN
hjic-943	278	14	is	be	AUX
hjic-943	278	15	unknown	unknown	ADJ
hjic-943	278	16	.	.	PUNCT
hjic-943	279	1	3	3	X
hjic-943	279	2	.	.	X
hjic-943	279	3	assume	assume	VERB
hjic-943	279	4	,	,	PUNCT
hjic-943	279	5	that	that	SCONJ
hjic-943	279	6	both	both	CCONJ
hjic-943	279	7	the	the	DET
hjic-943	279	8	mass	mass	NOUN
hjic-943	279	9	and	and	CCONJ
hjic-943	279	10	the	the	DET
hjic-943	279	11	internal	internal	ADJ
hjic-943	279	12	energy	energy	NOUN
hjic-943	279	13	of	of	ADP
hjic-943	279	14	liquid	liquid	NOUN
hjic-943	279	15	are	be	AUX
hjic-943	279	16	in	in	ADP
hjic-943	279	17	steady	steady	ADJ
hjic-943	279	18	state	state	NOUN
hjic-943	279	19	in	in	ADP
hjic-943	279	20	the	the	DET
hjic-943	279	21	tank	tank	NOUN
hjic-943	279	22	:	:	PUNCT
hjic-943	279	23	m	m	NOUN
hjic-943	279	24	'	'	PUNCT
hjic-943	279	25	~	~	SYM
hjic-943	279	26	0	0	NUM
hjic-943	279	27	and	and	CCONJ
hjic-943	279	28	u	u	ADJ
hjic-943	279	29	·	·	PUNCT
hjic-943	279	30	=	=	SYM
hjic-943	279	31	0	0	PUNCT
hjic-943	279	32	.	.	PUNCT
hjic-943	280	1	(	(	PUNCT
hjic-943	280	2	53	53	NUM
hjic-943	280	3	)	)	PUNCT
hjic-943	280	4	in	in	ADP
hjic-943	280	5	this	this	DET
hjic-943	280	6	case	case	NOUN
hjic-943	280	7	both	both	CCONJ
hjic-943	280	8	vertex	vertex	NOUN
hjic-943	280	9	m	m	NOUN
hjic-943	280	10	'	'	PUNCT
hjic-943	280	11	and	and	CCONJ
hjic-943	280	12	vertex	vertex	NOUN
hjic-943	280	13	u	u	NOUN
hjic-943	280	14	'	'	PUNCT
hjic-943	280	15	become	become	AUX
hjic-943	280	16	labelled	label	VERB
hjic-943	280	17	by	by	ADP
hjic-943	280	18	type	type	NOUN
hjic-943	280	19	<	<	X
hjic-943	280	20	g	g	PROPN
hjic-943	280	21	>	>	X
hjic-943	280	22	because	because	SCONJ
hjic-943	280	23	of	of	ADP
hjic-943	280	24	their	their	PRON
hjic-943	280	25	values	value	NOUN
hjic-943	280	26	are	be	AUX
hjic-943	280	27	equal	equal	ADJ
hjic-943	280	28	to	to	ADP
hjic-943	280	29	zero	zero	NUM
hjic-943	280	30	.	.	PUNCT
hjic-943	281	1	for	for	ADP
hjic-943	281	2	the	the	DET
hjic-943	281	3	appropriate	appropriate	ADJ
hjic-943	281	4	modification	modification	NOUN
hjic-943	281	5	of	of	ADP
hjic-943	281	6	the	the	DET
hjic-943	281	7	model	model	NOUN
hjic-943	281	8	specification	specification	NOUN
hjic-943	281	9	two	two	NUM
hjic-943	281	10	vertices	vertex	NOUN
hjic-943	281	11	must	must	AUX
hjic-943	281	12	be	be	AUX
hjic-943	281	13	found	find	VERB
hjic-943	281	14	on	on	ADP
hjic-943	281	15	the	the	DET
hjic-943	281	16	original	original	ADJ
hjic-943	281	17	representation	representation	NOUN
hjic-943	281	18	graph	graph	NOUN
hjic-943	281	19	(	(	PUNCT
hjic-943	281	20	fig.4a	fig.4a	NOUN
hjic-943	281	21	)	)	PUNCT
hjic-943	281	22	which	which	PRON
hjic-943	281	23	are	be	AUX
hjic-943	281	24	labelled	label	VERB
hjic-943	281	25	by	by	ADP
hjic-943	281	26	type	type	NOUN
hjic-943	281	27	<	<	X
hjic-943	281	28	s	s	X
hjic-943	281	29	>	>	X
hjic-943	281	30	or	or	CCONJ
hjic-943	281	31	<	<	X
hjic-943	281	32	s	s	X
hjic-943	281	33	*	*	X
hjic-943	281	34	>	>	X
hjic-943	281	35	and	and	CCONJ
hjic-943	281	36	from	from	ADP
hjic-943	281	37	which	which	PRON
hjic-943	281	38	two	two	NUM
hjic-943	281	39	directed	direct	VERB
hjic-943	281	40	paths	path	NOUN
hjic-943	281	41	start	start	VERB
hjic-943	281	42	into	into	ADP
hjic-943	281	43	m	m	PROPN
hjic-943	281	44	'	'	PUNCT
hjic-943	281	45	and	and	CCONJ
hjic-943	281	46	u	u	NOUN
hjic-943	281	47	'	'	PUNCT
hjic-943	281	48	.	.	PUNCT
hjic-943	282	1	these	these	DET
hjic-943	282	2	paths	path	NOUN
hjic-943	282	3	must	must	AUX
hjic-943	282	4	be	be	AUX
hjic-943	282	5	vertex	vertex	NOUN
hjic-943	282	6	-	-	PUNCT
hjic-943	282	7	disjoint	disjoint	NOUN
hjic-943	282	8	with	with	ADP
hjic-943	282	9	the	the	DET
hjic-943	282	10	original	original	ADJ
hjic-943	282	11	menger	menger	NOUN
hjic-943	282	12	-	-	PUNCT
hjic-943	282	13	type	type	NOUN
hjic-943	282	14	complete	complete	ADJ
hjic-943	282	15	linking	linking	NOUN
hjic-943	282	16	(	(	PUNCT
hjic-943	282	17	see	see	VERB
hjic-943	282	18	fig.4b	fig.4b	NOUN
hjic-943	282	19	)	)	PUNCT
hjic-943	282	20	.	.	PUNCT
hjic-943	283	1	let	let	VERB
hjic-943	283	2	m	m	PRON
hjic-943	283	3	and	and	CCONJ
hjic-943	283	4	u	u	PROPN
hjic-943	283	5	or	or	CCONJ
hjic-943	283	6	f	f	PROPN
hjic-943	283	7	and	and	CCONJ
hjic-943	283	8	q	q	PROPN
hjic-943	283	9	be	be	AUX
hjic-943	283	10	the	the	DET
hjic-943	283	11	chosen	choose	VERB
hjic-943	283	12	variable	variable	ADJ
hjic-943	283	13	pairs	pair	NOUN
hjic-943	283	14	.	.	PUNCT
hjic-943	284	1	dropping	drop	VERB
hjic-943	284	2	the	the	DET
hjic-943	284	3	original	original	ADJ
hjic-943	284	4	label	label	NOUN
hjic-943	284	5	of	of	ADP
hjic-943	284	6	these	these	DET
hjic-943	284	7	vertices	vertex	NOUN
hjic-943	284	8	means	mean	VERB
hjic-943	284	9	that	that	SCONJ
hjic-943	284	10	these	these	DET
hjic-943	284	11	variables	variable	NOUN
hjic-943	284	12	are	be	AUX
hjic-943	284	13	considered	consider	VERB
hjic-943	284	14	to	to	PART
hjic-943	284	15	be	be	AUX
hjic-943	284	16	unknown	unknown	ADJ
hjic-943	284	17	.	.	PUNCT
hjic-943	285	1	reduced	reduce	VERB
hjic-943	285	2	graphs	graph	NOUN
hjic-943	285	3	are	be	AUX
hjic-943	285	4	shown	show	VERB
hjic-943	285	5	in	in	ADP
hjic-943	285	6	figs.ba	figs.ba	X
hjic-943	285	7	and	and	CCONJ
hjic-943	285	8	bb	bb	NOUN
hjic-943	285	9	.	.	PUNCT
hjic-943	285	10	assuming	assume	VERB
hjic-943	285	11	steady	steady	ADJ
hjic-943	285	12	state	state	NOUN
hjic-943	285	13	for	for	ADP
hjic-943	285	14	a	a	DET
hjic-943	285	15	state	state	NOUN
hjic-943	285	16	variable	variable	NOUN
hjic-943	285	17	x	x	NOUN
hjic-943	285	18	,	,	PUNCT
hjic-943	285	19	the	the	DET
hjic-943	285	20	most	most	ADV
hjic-943	285	21	usual	usual	ADJ
hjic-943	285	22	modification	modification	NOUN
hjic-943	285	23	of	of	ADP
hjic-943	285	24	the	the	DET
hjic-943	285	25	specification	specification	NOUN
hjic-943	285	26	in	in	ADP
hjic-943	285	27	the	the	DET
hjic-943	285	28	modelling	modelling	NOUN
hjic-943	285	29	practice	practice	NOUN
hjic-943	285	30	is	be	AUX
hjic-943	285	31	to	to	PART
hjic-943	285	32	drop	drop	VERB
hjic-943	285	33	the	the	DET
hjic-943	285	34	initial	initial	ADJ
hjic-943	285	35	value	value	NOUN
hjic-943	285	36	of	of	ADP
hjic-943	285	37	variable	variable	NOUN
hjic-943	285	38	x	x	NUM
hjic-943	285	39	from	from	ADP
hjic-943	285	40	the	the	DET
hjic-943	285	41	specification	specification	NOUN
hjic-943	285	42	.	.	PUNCT
hjic-943	286	1	the	the	DET
hjic-943	286	2	above	above	ADJ
hjic-943	286	3	example	example	NOUN
hjic-943	286	4	illustrates	illustrate	VERB
hjic-943	286	5	that	that	SCONJ
hjic-943	286	6	there	there	PRON
hjic-943	286	7	can	can	AUX
hjic-943	286	8	be	be	AUX
hjic-943	286	9	many	many	ADJ
hjic-943	286	10	other	other	ADJ
hjic-943	286	11	modifications	modification	NOUN
hjic-943	286	12	of	of	ADP
hjic-943	286	13	the	the	DET
hjic-943	286	14	specification	specification	NOUN
hjic-943	286	15	which	which	PRON
hjic-943	286	16	yield	yield	VERB
hjic-943	286	17	a	a	DET
hjic-943	286	18	structurally	structurally	ADV
hjic-943	286	19	solvable	solvable	ADJ
hjic-943	286	20	model	model	NOUN
hjic-943	286	21	.	.	PUNCT
hjic-943	287	1	the	the	DET
hjic-943	287	2	69	69	NUM
hjic-943	287	3	representation	representation	NOUN
hjic-943	287	4	graph	graph	NOUN
hjic-943	287	5	is	be	AUX
hjic-943	287	6	a	a	DET
hjic-943	287	7	very	very	ADV
hjic-943	287	8	suitable	suitable	ADJ
hjic-943	287	9	tool	tool	NOUN
hjic-943	287	10	to	to	PART
hjic-943	287	11	find	find	VERB
hjic-943	287	12	these	these	DET
hjic-943	287	13	possible	possible	ADJ
hjic-943	287	14	modifications	modification	NOUN
hjic-943	287	15	of	of	ADP
hjic-943	287	16	the	the	DET
hjic-943	287	17	original	original	ADJ
hjic-943	287	18	specification	specification	NOUN
hjic-943	287	19	.	.	PUNCT
hjic-943	288	1	steady	steady	ADJ
hjic-943	288	2	state	state	NOUN
hjic-943	288	3	assumption	assumption	NOUN
hjic-943	288	4	for	for	ADP
hjic-943	288	5	models	model	NOUN
hjic-943	288	6	with	with	ADP
hjic-943	288	7	dijferential	dijferential	ADJ
hjic-943	288	8	index	index	NOUN
hjic-943	288	9	2	2	NUM
hjic-943	288	10	consider	consider	VERB
hjic-943	288	11	a	a	DET
hjic-943	288	12	dynamic	dynamic	ADJ
hjic-943	288	13	process	process	NOUN
hjic-943	288	14	model	model	NOUN
hjic-943	288	15	described	describe	VERB
hjic-943	288	16	by	by	ADP
hjic-943	288	17	a	a	DET
hjic-943	288	18	semi­	semi­	ADJ
hjic-943	288	19	explicit	explicit	ADJ
hjic-943	288	20	dae	dae	NOUN
hjic-943	288	21	system	system	NOUN
hjic-943	288	22	,	,	PUNCT
hjic-943	288	23	which	which	PRON
hjic-943	288	24	has	have	VERB
hjic-943	288	25	differential	differential	ADJ
hjic-943	288	26	index	index	NOUN
hjic-943	288	27	2	2	NUM
hjic-943	288	28	.	.	PUNCT
hjic-943	289	1	the	the	DET
hjic-943	289	2	representation	representation	NOUN
hjic-943	289	3	graph	graph	NOUN
hjic-943	289	4	corresponding	correspond	VERB
hjic-943	289	5	to	to	ADP
hjic-943	289	6	the	the	DET
hjic-943	289	7	standard	standard	ADJ
hjic-943	289	8	forni	forni	PROPN
hjic-943	289	9	0f	0f	PROPN
hjic-943	289	10	the	the	DET
hjic-943	289	11	model	model	NOUN
hjic-943	289	12	contains	contain	VERB
hjic-943	289	13	an	an	DET
hjic-943	289	14	underspecifled	underspecifled	ADJ
hjic-943	289	15	and	and	CCONJ
hjic-943	289	16	an	an	DET
hjic-943	289	17	overspecified	overspecified	ADJ
hjic-943	289	18	part	part	NOUN
hjic-943	289	19	.	.	PUNCT
hjic-943	290	1	assume	assume	VERB
hjic-943	290	2	that	that	SCONJ
hjic-943	290	3	a	a	DET
hjic-943	290	4	state	state	NOUN
hjic-943	290	5	variable	variable	NOUN
hjic-943	290	6	x	x	PUNCT
hjic-943	290	7	being	be	AUX
hjic-943	290	8	on	on	ADP
hjic-943	290	9	the	the	DET
hjic-943	290	10	underspecified	underspecified	ADJ
hjic-943	290	11	subgraph	subgraph	NOUN
hjic-943	290	12	is	be	AUX
hjic-943	290	13	in	in	ADP
hjic-943	290	14	steady	steady	ADJ
hjic-943	290	15	state	state	NOUN
hjic-943	290	16	.	.	PUNCT
hjic-943	291	1	then	then	ADV
hjic-943	291	2	the	the	DET
hjic-943	291	3	following	follow	VERB
hjic-943	291	4	proposition	proposition	NOUN
hjic-943	291	5	is	be	AUX
hjic-943	291	6	true	true	ADJ
hjic-943	291	7	.	.	PUNCT
hjic-943	292	1	proposition	proposition	NOUN
hjic-943	292	2	2	2	NUM
hjic-943	292	3	:	:	PUNCT
hjic-943	292	4	consider	consider	VERB
hjic-943	292	5	a	a	DET
hjic-943	292	6	standard	standard	ADJ
hjic-943	292	7	form	form	NOUN
hjic-943	292	8	dynamic	dynamic	ADJ
hjic-943	292	9	model	model	NOUN
hjic-943	292	10	described	describe	VERB
hjic-943	292	11	by	by	ADP
hjic-943	292	12	a	a	DET
hjic-943	292	13	semi	semi	ADJ
hjic-943	292	14	-	-	ADJ
hjic-943	292	15	explicit	explicit	ADJ
hjic-943	292	16	dab	dab	NOUN
hjic-943	292	17	-	-	PUNCT
hjic-943	292	18	system	system	NOUN
hjic-943	292	19	,	,	PUNCT
hjic-943	292	20	which	which	PRON
hjic-943	292	21	has	have	VERB
hjic-943	292	22	difierential	difierential	ADJ
hjic-943	292	23	index	index	NOUN
hjic-943	292	24	2	2	NUM
hjic-943	292	25	.	.	PUNCT
hjic-943	292	26	assume	assume	VERB
hjic-943	292	27	that	that	SCONJ
hjic-943	292	28	the	the	DET
hjic-943	292	29	generality	generality	NOUN
hjic-943	292	30	assumption	assumption	NOUN
hjic-943	292	31	ga	ga	PROPN
hjic-943	292	32	is	be	AUX
hjic-943	292	33	true	true	ADJ
hjic-943	292	34	for	for	ADP
hjic-943	292	35	the	the	DET
hjic-943	292	36	algebraic	algebraic	ADJ
hjic-943	292	37	part	part	NOUN
hjic-943	292	38	of	of	ADP
hjic-943	292	39	the	the	DET
hjic-943	292	40	model	model	NOUN
hjic-943	292	41	.	.	PUNCT
hjic-943	293	1	consider	consider	VERB
hjic-943	293	2	the	the	DET
hjic-943	293	3	dynamic	dynamic	ADJ
hjic-943	293	4	representation	representation	NOUN
hjic-943	293	5	graph	graph	NOUN
hjic-943	293	6	of	of	ADP
hjic-943	293	7	the	the	DET
hjic-943	293	8	model	model	NOUN
hjic-943	293	9	.	.	PUNCT
hjic-943	294	1	assume	assume	VERB
hjic-943	294	2	that	that	SCONJ
hjic-943	294	3	there	there	PRON
hjic-943	294	4	is	be	VERB
hjic-943	294	5	only	only	ADV
hjic-943	294	6	one	one	NUM
hjic-943	294	7	initial	initial	ADJ
hjic-943	294	8	vertex	vertex	NOUN
hjic-943	294	9	without	without	ADP
hjic-943	294	10	label	label	NOUN
hjic-943	294	11	<	<	X
hjic-943	294	12	s	s	X
hjic-943	294	13	>	>	X
hjic-943	294	14	on	on	ADP
hjic-943	294	15	the	the	DET
hjic-943	294	16	underspecified	underspecified	ADJ
hjic-943	294	17	part	part	NOUN
hjic-943	294	18	of	of	ADP
hjic-943	294	19	static	static	ADJ
hjic-943	294	20	graphs	graph	NOUN
hjic-943	294	21	.	.	PUNCT
hjic-943	295	1	let	let	VERB
hjic-943	295	2	x	x	X
hjic-943	295	3	'	'	PUNCT
hjic-943	295	4	be	be	AUX
hjic-943	295	5	a	a	DET
hjic-943	295	6	derivative	derivative	ADJ
hjic-943	295	7	variable	variable	NOUN
hjic-943	295	8	also	also	ADV
hjic-943	295	9	on	on	ADP
hjic-943	295	10	the	the	DET
hjic-943	295	11	underspecified	underspecified	ADJ
hjic-943	295	12	subgraph	subgraph	NOUN
hjic-943	295	13	.	.	PUNCT
hjic-943	296	1	assume	assume	VERB
hjic-943	296	2	that	that	SCONJ
hjic-943	296	3	the	the	DET
hjic-943	296	4	state	state	NOUN
hjic-943	296	5	variable	variable	NOUN
hjic-943	296	6	xis	xis	PROPN
hjic-943	296	7	in	in	ADP
hjic-943	296	8	steady	steady	ADJ
hjic-943	296	9	state	state	NOUN
hjic-943	296	10	,	,	PUNCT
hjic-943	296	11	so	so	ADV
hjic-943	296	12	let	let	VERB
hjic-943	296	13	the	the	DET
hjic-943	296	14	value	value	NOUN
hjic-943	296	15	of	of	ADP
hjic-943	296	16	derivative	derivative	ADJ
hjic-943	296	17	variable	variable	NOUN
hjic-943	296	18	x	x	NOUN
hjic-943	296	19	'	'	PUNCT
hjic-943	296	20	be	be	AUX
hjic-943	296	21	equal	equal	ADJ
hjic-943	296	22	to	to	ADP
hjic-943	296	23	zero	zero	NUM
hjic-943	296	24	.	.	PUNCT
hjic-943	297	1	hence	hence	ADV
hjic-943	297	2	let	let	VERB
hjic-943	297	3	the	the	DET
hjic-943	297	4	label	label	NOUN
hjic-943	297	5	of	of	ADP
hjic-943	297	6	x	x	NOUN
hjic-943	297	7	'	'	PUNCT
hjic-943	297	8	be	be	AUX
hjic-943	297	9	type	type	NOUN
hjic-943	297	10	<	<	X
hjic-943	297	11	g	g	PROPN
hjic-943	297	12	>	>	X
hjic-943	297	13	.then	.then	NOUN
hjic-943	297	14	:	:	PUNCT
hjic-943	297	15	1	1	X
hjic-943	297	16	.	.	X
hjic-943	297	17	static	static	ADJ
hjic-943	297	18	graphs	graph	NOUN
hjic-943	297	19	at	at	ADP
hjic-943	297	20	any	any	DET
hjic-943	297	21	time	time	NOUN
hjic-943	297	22	step	step	NOUN
hjic-943	297	23	t	t	NOUN
hjic-943	297	24	are	be	AUX
hjic-943	297	25	overspecifled	overspecifle	VERB
hjic-943	297	26	,	,	PUNCT
hjic-943	297	27	hence	hence	ADV
hjic-943	297	28	there	there	PRON
hjic-943	297	29	are	be	VERB
hjic-943	297	30	no	no	DET
hjic-943	297	31	menger	menger	NOUN
hjic-943	297	32	-	-	PUNCT
hjic-943	297	33	type	type	NOUN
hjic-943	297	34	complete	complete	ADJ
hjic-943	297	35	linking	linking	NOUN
hjic-943	297	36	on	on	ADP
hjic-943	297	37	them	they	PRON
hjic-943	297	38	.	.	PUNCT
hjic-943	298	1	2	2	X
hjic-943	298	2	.	.	X
hjic-943	298	3	modify	modify	VERB
hjic-943	298	4	the	the	DET
hjic-943	298	5	specification	specification	NOUN
hjic-943	298	6	of	of	ADP
hjic-943	298	7	the	the	DET
hjic-943	298	8	model	model	NOUN
hjic-943	298	9	as	as	SCONJ
hjic-943	298	10	follows	follow	VERB
hjic-943	298	11	:	:	PUNCT
hjic-943	298	12	look	look	VERB
hjic-943	298	13	for	for	ADP
hjic-943	298	14	a	a	DET
hjic-943	298	15	variable	variable	ADJ
hjic-943	298	16	vertex	vertex	NOUN
hjic-943	298	17	xk	xk	PROPN
hjic-943	298	18	on	on	ADP
hjic-943	298	19	the	the	DET
hjic-943	298	20	overspedfied	overspedfied	ADJ
hjic-943	298	21	part	part	NOUN
hjic-943	298	22	which	which	PRON
hjic-943	298	23	has	have	AUX
hjic-943	298	24	label	label	VERB
hjic-943	298	25	<	<	X
hjic-943	298	26	s	s	X
hjic-943	298	27	>	>	X
hjic-943	298	28	or	or	CCONJ
hjic-943	298	29	<	<	X
hjic-943	298	30	s	s	PROPN
hjic-943	298	31	*	*	X
hjic-943	298	32	>	>	X
hjic-943	298	33	and	and	CCONJ
hjic-943	298	34	drop	drop	VERB
hjic-943	298	35	this	this	DET
hjic-943	298	36	label	label	NOUN
hjic-943	298	37	of	of	ADP
hjic-943	298	38	xk	xk	PROPN
hjic-943	298	39	.	.	PROPN
hjic-943	299	1	then	then	ADV
hjic-943	299	2	xk	xk	PROPN
hjic-943	299	3	becomes	become	VERB
hjic-943	299	4	an	an	DET
hjic-943	299	5	unknown	unknown	ADJ
hjic-943	299	6	variable	variable	NOUN
hjic-943	299	7	.	.	PUNCT
hjic-943	300	1	the	the	DET
hjic-943	300	2	modified	modify	VERB
hjic-943	300	3	model	model	NOUN
hjic-943	300	4	is	be	AUX
hjic-943	300	5	then	then	ADV
hjic-943	300	6	structurally	structurally	ADV
hjic-943	300	7	solvable	solvable	ADJ
hjic-943	300	8	.	.	PUNCT
hjic-943	301	1	proof	proof	NOUN
hjic-943	301	2	:	:	PUNCT
hjic-943	302	1	1	1	X
hjic-943	302	2	.	.	X
hjic-943	302	3	it	it	PRON
hjic-943	302	4	follows	follow	VERB
hjic-943	302	5	from	from	ADP
hjic-943	302	6	the	the	DET
hjic-943	302	7	procedure	procedure	NOUN
hjic-943	302	8	in	in	ADP
hjic-943	302	9	proposition	proposition	NOUN
hjic-943	302	10	2	2	NUM
hjic-943	302	11	that	that	SCONJ
hjic-943	302	12	the	the	DET
hjic-943	302	13	overspecified	overspecified	ADJ
hjic-943	302	14	subgraph	subgraph	NOUN
hjic-943	302	15	is	be	AUX
hjic-943	302	16	unchanged	unchanged	ADJ
hjic-943	302	17	while	while	SCONJ
hjic-943	302	18	the	the	DET
hjic-943	302	19	underspecification	underspecification	NOUN
hjic-943	302	20	of	of	ADP
hjic-943	302	21	the	the	DET
hjic-943	302	22	originally	originally	ADV
hjic-943	302	23	underspecified	underspecified	ADJ
hjic-943	302	24	part	part	NOUN
hjic-943	302	25	disappears	disappear	VERB
hjic-943	302	26	.	.	PUNCT
hjic-943	303	1	2	2	X
hjic-943	303	2	.	.	X
hjic-943	303	3	variable	variable	NOUN
hjic-943	303	4	x	x	NOUN
hjic-943	303	5	'	'	PUNCT
hjic-943	303	6	has	have	AUX
hjic-943	303	7	label	label	VERB
hjic-943	303	8	<	<	X
hjic-943	303	9	g	g	PROPN
hjic-943	303	10	>	>	X
hjic-943	303	11	therefore	therefore	ADV
hjic-943	303	12	there	there	PRON
hjic-943	303	13	is	be	VERB
hjic-943	303	14	a	a	DET
hjic-943	303	15	directed	direct	VERB
hjic-943	303	16	path	path	NOUN
hjic-943	303	17	from	from	ADP
hjic-943	303	18	an	an	DET
hjic-943	303	19	initial	initial	ADJ
hjic-943	303	20	vertex	vertex	NOUN
hjic-943	303	21	having	have	VERB
hjic-943	303	22	neither	neither	CCONJ
hjic-943	303	23	label	label	VERB
hjic-943	303	24	<	<	X
hjic-943	303	25	s	s	X
hjic-943	303	26	>	>	X
hjic-943	303	27	nor	nor	CCONJ
hjic-943	303	28	<	<	X
hjic-943	303	29	s	s	PROPN
hjic-943	303	30	*	*	X
hjic-943	303	31	>	>	X
hjic-943	303	32	into	into	ADP
hjic-943	303	33	vertex	vertex	NOUN
hjic-943	303	34	x	x	NOUN
hjic-943	303	35	'	'	PUNCT
hjic-943	303	36	on	on	ADP
hjic-943	303	37	the	the	DET
hjic-943	303	38	originally	originally	ADV
hjic-943	303	39	underspecified	underspecified	ADJ
hjic-943	303	40	subgraph	subgraph	NOUN
hjic-943	303	41	.	.	PUNCT
hjic-943	304	1	furthermore	furthermore	ADV
hjic-943	304	2	,	,	PUNCT
hjic-943	304	3	there	there	PRON
hjic-943	304	4	is	be	VERB
hjic-943	304	5	a	a	DET
hjic-943	304	6	new	new	ADJ
hjic-943	304	7	directed	direct	VERB
hjic-943	304	8	path	path	NOUN
hjic-943	304	9	from	from	ADP
hjic-943	304	10	xt	xt	PROPN
hjic-943	304	11	into	into	ADP
hjic-943	304	12	a	a	DET
hjic-943	304	13	vertex	vertex	NOUN
hjic-943	304	14	with	with	ADP
hjic-943	304	15	label	label	NOUN
hjic-943	304	16	<	<	X
hjic-943	304	17	g	g	X
hjic-943	304	18	>	>	X
hjic-943	304	19	on	on	ADP
hjic-943	304	20	the	the	DET
hjic-943	304	21	originally	originally	ADV
hjic-943	304	22	underspecified	underspecified	ADJ
hjic-943	304	23	subgraph	subgraph	NOUN
hjic-943	304	24	as	as	ADP
hjic-943	304	25	result	result	NOUN
hjic-943	304	26	of	of	ADP
hjic-943	304	27	the	the	DET
hjic-943	304	28	described	describe	VERB
hjic-943	304	29	modification	modification	NOUN
hjic-943	304	30	of	of	ADP
hjic-943	304	31	specification	specification	NOUN
hjic-943	304	32	.	.	PUNCT
hjic-943	305	1	these	these	DET
hjic-943	305	2	directed	direct	VERB
hjic-943	305	3	paths	path	NOUN
hjic-943	305	4	together	together	ADV
hjic-943	305	5	with	with	ADP
hjic-943	305	6	a	a	DET
hjic-943	305	7	maximal	maximal	ADJ
hjic-943	305	8	menger~	menger~	ADJ
hjic-943	305	9	type	type	NOUN
hjic-943	305	10	complete	complete	ADJ
hjic-943	305	11	linking	linking	NOUN
hjic-943	305	12	of	of	ADP
hjic-943	305	13	the	the	DET
hjic-943	305	14	original	original	ADJ
hjic-943	305	15	graph	graph	NOUN
hjic-943	305	16	yield	yield	VERB
hjic-943	305	17	a	a	DET
hjic-943	305	18	menger	menger	NOUN
hjic-943	305	19	-	-	PUNCT
hjic-943	305	20	type	type	NOUN
hjic-943	305	21	complete	complete	ADJ
hjic-943	305	22	linking	linking	NOUN
hjic-943	305	23	on	on	ADP
hjic-943	305	24	the	the	DET
hjic-943	305	25	modified	modify	VERB
hjic-943	305	26	graph	graph	NOUN
hjic-943	305	27	.	.	PUNCT
hjic-943	306	1	hence	hence	ADV
hjic-943	306	2	the	the	DET
hjic-943	306	3	modified	modify	VERB
hjic-943	306	4	model	model	NOUN
hjic-943	306	5	is	be	AUX
hjic-943	306	6	structurally	structurally	ADV
hjic-943	306	7	solvable	solvable	ADJ
hjic-943	306	8	.	.	PUNCT
hjic-943	307	1	consequence	consequence	NOUN
hjic-943	307	2	:	:	PUNCT
hjic-943	307	3	the	the	DET
hjic-943	307	4	differential	differential	ADJ
hjic-943	307	5	index	index	NOUN
hjic-943	307	6	of	of	ADP
hjic-943	307	7	modified	modified	ADJ
hjic-943	307	8	model	model	NOUN
hjic-943	307	9	corresponding	correspond	VERB
hjic-943	307	10	to	to	PART
hjic-943	307	11	proposition	proposition	NOUN
hjic-943	307	12	2	2	NUM
hjic-943	307	13	decreases	decrease	NOUN
hjic-943	307	14	from	from	ADP
hjic-943	307	15	2	2	NUM
hjic-943	307	16	to	to	ADP
hjic-943	307	17	1	1	NUM
hjic-943	307	18	.	.	PUNCT
hjic-943	307	19	70	70	NUM
hjic-943	307	20	u~~	u~~	ADJ
hjic-943	307	21	f	f	PROPN
hjic-943	307	22	---------ih	---------ih	NOUN
hjic-943	307	23	<	<	X
hjic-943	307	24	~~	~~	X
hjic-943	307	25	q	q	X
hjic-943	307	26	~	~	X
hjic-943	307	27	du	du	X
hjic-943	307	28	<	<	X
hjic-943	307	29	g	g	X
hjic-943	307	30	>	>	X
hjic-943	307	31	a	a	DET
hjic-943	307	32	,	,	PUNCT
hjic-943	307	33	b	b	NOUN
hjic-943	307	34	,	,	PUNCT
hjic-943	307	35	fig.9	fig.9	ADJ
hjic-943	307	36	reduced	reduce	VERB
hjic-943	307	37	graph	graph	NOUN
hjic-943	307	38	of	of	ADP
hjic-943	307	39	model	model	NOUN
hjic-943	307	40	in	in	ADP
hjic-943	307	41	example	example	NOUN
hjic-943	307	42	2	2	NUM
hjic-943	307	43	with	with	ADP
hjic-943	307	44	specification	specification	NOUN
hjic-943	307	45	2	2	NUM
hjic-943	307	46	;	;	PUNCT
hjic-943	307	47	a	a	PRON
hjic-943	307	48	,	,	PUNCT
hjic-943	307	49	assuming	assume	VERB
hjic-943	307	50	steady	steady	ADJ
hjic-943	307	51	state	state	NOUN
hjic-943	307	52	for	for	ADP
hjic-943	307	53	u	u	NOUN
hjic-943	307	54	;	;	PUNCT
hjic-943	307	55	b	b	NUM
hjic-943	307	56	,	,	PUNCT
hjic-943	307	57	assuming	assume	VERB
hjic-943	307	58	steady	steady	ADJ
hjic-943	307	59	state	state	NOUN
hjic-943	307	60	for	for	ADP
hjic-943	307	61	m	m	PROPN
hjic-943	307	62	example	example	NOUN
hjic-943	307	63	2	2	NUM
hjic-943	307	64	(	(	PUNCT
hjic-943	307	65	continued	continue	VERB
hjic-943	307	66	)	)	PUNCT
hjic-943	307	67	.	.	PUNCT
hjic-943	308	1	consider	consider	VERB
hjic-943	308	2	example	example	NOUN
hjic-943	308	3	2	2	NUM
hjic-943	308	4	with	with	ADP
hjic-943	308	5	specification	specification	NOUN
hjic-943	308	6	2	2	NUM
hjic-943	308	7	.	.	PUNCT
hjic-943	309	1	the	the	DET
hjic-943	309	2	differential	differential	ADJ
hjic-943	309	3	index	index	NOUN
hjic-943	309	4	of	of	ADP
hjic-943	309	5	this	this	DET
hjic-943	309	6	model	model	NOUN
hjic-943	309	7	is	be	AUX
hjic-943	309	8	equal	equal	ADJ
hjic-943	309	9	to	to	ADP
hjic-943	309	10	2	2	NUM
hjic-943	309	11	.	.	PUNCT
hjic-943	309	12	assume	assume	VERB
hjic-943	309	13	that	that	SCONJ
hjic-943	309	14	the	the	DET
hjic-943	309	15	internal	internal	ADJ
hjic-943	309	16	energy	energy	NOUN
hjic-943	309	17	of	of	ADP
hjic-943	309	18	liquid	liquid	NOUN
hjic-943	309	19	is	be	AUX
hjic-943	309	20	in	in	ADP
hjic-943	309	21	steady	steady	ADJ
hjic-943	309	22	state	state	NOUN
hjic-943	309	23	in	in	ADP
hjic-943	309	24	the	the	DET
hjic-943	309	25	tank	tank	NOUN
hjic-943	309	26	:	:	PUNCT
hjic-943	309	27	u	u	NOUN
hjic-943	309	28	·	·	PUNCT
hjic-943	309	29	:	:	PUNCT
hjic-943	309	30	:	:	PUNCT
hjic-943	309	31	:	:	PUNCT
hjic-943	309	32	:o	:o	PROPN
hjic-943	309	33	(	(	PUNCT
hjic-943	309	34	54	54	NUM
hjic-943	309	35	)	)	PUNCT
hjic-943	309	36	then	then	ADV
hjic-943	309	37	the	the	DET
hjic-943	309	38	value	value	NOUN
hjic-943	309	39	of	of	ADP
hjic-943	309	40	derivative	derivative	ADJ
hjic-943	309	41	variable	variable	ADJ
hjic-943	309	42	u	u	NOUN
hjic-943	309	43	'	'	PUNCT
hjic-943	309	44	is	be	AUX
hjic-943	309	45	equal	equal	ADJ
hjic-943	309	46	to	to	ADP
hjic-943	309	47	zero	zero	NUM
hjic-943	309	48	,	,	PUNCT
hjic-943	309	49	so	so	ADV
hjic-943	309	50	let	let	VERB
hjic-943	309	51	the	the	DET
hjic-943	309	52	label	label	NOUN
hjic-943	309	53	of	of	ADP
hjic-943	309	54	vertex	vertex	NOUN
hjic-943	309	55	u	u	NOUN
hjic-943	309	56	'	'	PUNCT
hjic-943	309	57	be	be	AUX
hjic-943	309	58	type	type	NOUN
hjic-943	309	59	<	<	X
hjic-943	309	60	g	g	X
hjic-943	309	61	>	>	X
hjic-943	309	62	on	on	ADP
hjic-943	309	63	all	all	DET
hjic-943	309	64	static	static	ADJ
hjic-943	309	65	graphs	graph	NOUN
hjic-943	309	66	.	.	PUNCT
hjic-943	310	1	hence	hence	ADV
hjic-943	310	2	the	the	DET
hjic-943	310	3	underspecification	underspecification	NOUN
hjic-943	310	4	of	of	ADP
hjic-943	310	5	the	the	DET
hjic-943	310	6	originally	originally	ADV
hjic-943	310	7	underspecified	underspecified	ADJ
hjic-943	310	8	subgraph	subgraph	NOUN
hjic-943	310	9	disappears	disappear	VERB
hjic-943	310	10	.	.	PUNCT
hjic-943	311	1	modify	modify	VERB
hjic-943	311	2	the	the	DET
hjic-943	311	3	model	model	NOUN
hjic-943	311	4	specification	specification	NOUN
hjic-943	311	5	according	accord	VERB
hjic-943	311	6	to	to	ADP
hjic-943	311	7	proposition	proposition	NOUN
hjic-943	311	8	2	2	NUM
hjic-943	311	9	.	.	PUNCT
hjic-943	312	1	there	there	PRON
hjic-943	312	2	are	be	VERB
hjic-943	312	3	4	4	NUM
hjic-943	312	4	vertices	vertex	NOUN
hjic-943	312	5	with	with	ADP
hjic-943	312	6	label	label	NOUN
hjic-943	312	7	<	<	X
hjic-943	312	8	s	s	X
hjic-943	312	9	>	>	X
hjic-943	312	10	or	or	CCONJ
hjic-943	312	11	<	<	X
hjic-943	312	12	s	s	X
hjic-943	312	13	*	*	X
hjic-943	312	14	>	>	X
hjic-943	312	15	(	(	PUNCT
hjic-943	312	16	m	m	PROPN
hjic-943	312	17	,	,	PUNCT
hjic-943	312	18	u	u	PROPN
hjic-943	312	19	,	,	PUNCT
hjic-943	312	20	tl	tl	PROPN
hjic-943	312	21	and	and	CCONJ
hjic-943	312	22	p	p	X
hjic-943	312	23	)	)	PUNCT
hjic-943	312	24	on	on	ADP
hjic-943	312	25	~e	~e	NUM
hjic-943	312	26	overspecified	overspecified	ADJ
hjic-943	312	27	subgraph	subgraph	NOUN
hjic-943	312	28	(	(	PUNCT
hjic-943	312	29	see	see	VERB
hjic-943	312	30	fig.5	fig.5	NOUN
hjic-943	312	31	)	)	PUNCT
hjic-943	312	32	.	.	PUNCT
hjic-943	313	1	drop	drop	VERB
hjic-943	313	2	the	the	DET
hjic-943	313	3	label	label	NOUN
hjic-943	313	4	<	<	X
hjic-943	313	5	s	s	X
hjic-943	313	6	>	>	X
hjic-943	313	7	of	of	ADP
hjic-943	313	8	vertex	vertex	NOUN
hjic-943	313	9	u	u	NOUN
hjic-943	313	10	for	for	ADP
hjic-943	313	11	example	example	NOUN
hjic-943	313	12	,	,	PUNCT
hjic-943	313	13	i.e.	i.e.	X
hjic-943	313	14	consider	consider	VERB
hjic-943	313	15	the	the	DET
hjic-943	313	16	initial	initial	ADJ
hjic-943	313	17	value	value	NOUN
hjic-943	313	18	of	of	ADP
hjic-943	313	19	internal	internal	ADJ
hjic-943	313	20	energy	energy	NOUN
hjic-943	313	21	of	of	ADP
hjic-943	313	22	liquid	liquid	NOUN
hjic-943	313	23	to	to	PART
hjic-943	313	24	be	be	AUX
hjic-943	313	25	unknown	unknown	ADJ
hjic-943	313	26	variable	variable	NOUN
hjic-943	313	27	in	in	ADP
hjic-943	313	28	the	the	DET
hjic-943	313	29	tank	tank	NOUN
hjic-943	313	30	.	.	PUNCT
hjic-943	314	1	the	the	DET
hjic-943	314	2	reduced	reduce	VERB
hjic-943	314	3	graph	graph	NOUN
hjic-943	314	4	of	of	ADP
hjic-943	314	5	modified	modify	VERB
hjic-943	314	6	model	model	NOUN
hjic-943	314	7	can	can	AUX
hjic-943	314	8	be	be	AUX
hjic-943	314	9	seen	see	VERB
hjic-943	314	10	in	in	ADP
hjic-943	314	11	fig	fig	NOUN
hjic-943	314	12	.	.	PUNCT
hjic-943	315	1	9a	9a	NOUN
hjic-943	315	2	.	.	PUNCT
hjic-943	316	1	there	there	PRON
hjic-943	316	2	is	be	VERB
hjic-943	316	3	a	a	DET
hjic-943	316	4	menger	menger	NOUN
hjic-943	316	5	-	-	PUNCT
hjic-943	316	6	type	type	NOUN
hjic-943	316	7	complete	complete	ADJ
hjic-943	316	8	linking	linking	NOUN
hjic-943	316	9	on	on	ADP
hjic-943	316	10	the	the	DET
hjic-943	316	11	reduced	reduce	VERB
hjic-943	316	12	graph~	graph~	PROPN
hjic-943	316	13	so	so	SCONJ
hjic-943	316	14	the	the	DET
hjic-943	316	15	standard	standard	ADJ
hjic-943	316	16	form	form	NOUN
hjic-943	316	17	of	of	ADP
hjic-943	316	18	modified	modify	VERB
hjic-943	316	19	model	model	NOUN
hjic-943	316	20	is	be	AUX
hjic-943	316	21	conditionally	conditionally	ADV
hjic-943	316	22	structurally	structurally	ADV
hjic-943	316	23	solvable	solvable	ADJ
hjic-943	316	24	.	.	PUNCT
hjic-943	317	1	hence	hence	ADV
hjic-943	317	2	the	the	DET
hjic-943	317	3	differential	differential	ADJ
hjic-943	317	4	index	index	NOUN
hjic-943	317	5	of	of	ADP
hjic-943	317	6	the	the	DET
hjic-943	317	7	modified	modify	VERB
hjic-943	317	8	model	model	NOUN
hjic-943	317	9	is	be	AUX
hjic-943	317	10	equal	equal	ADJ
hjic-943	317	11	to	to	ADP
hjic-943	317	12	1	1	NUM
hjic-943	317	13	.	.	PUNCT
hjic-943	318	1	the	the	DET
hjic-943	318	2	result	result	NOUN
hjic-943	318	3	is	be	AUX
hjic-943	318	4	the	the	DET
hjic-943	318	5	same	same	ADJ
hjic-943	318	6	if	if	SCONJ
hjic-943	318	7	we	we	PRON
hjic-943	318	8	drop	drop	VERB
hjic-943	318	9	the	the	DET
hjic-943	318	10	labels	label	NOUN
hjic-943	318	11	of	of	ADP
hjic-943	318	12	m	m	PROPN
hjic-943	318	13	,	,	PUNCT
hjic-943	318	14	tl	tl	PROPN
hjic-943	318	15	or	or	CCONJ
hjic-943	318	16	p	p	NOUN
hjic-943	318	17	during	during	ADP
hjic-943	318	18	the	the	DET
hjic-943	318	19	modification	modification	NOUN
hjic-943	318	20	of	of	ADP
hjic-943	318	21	specification	specification	NOUN
hjic-943	318	22	.	.	PUNCT
hjic-943	319	1	it	it	PRON
hjic-943	319	2	can	can	AUX
hjic-943	319	3	be	be	AUX
hjic-943	319	4	seen	see	VERB
hjic-943	319	5	,	,	PUNCT
hjic-943	319	6	that	that	SCONJ
hjic-943	319	7	the	the	DET
hjic-943	319	8	differential	differential	ADJ
hjic-943	319	9	index	index	NOUN
hjic-943	319	10	of	of	ADP
hjic-943	319	11	the	the	DET
hjic-943	319	12	standard	standard	ADJ
hjic-943	319	13	model	model	NOUN
hjic-943	319	14	decreases	decrease	VERB
hjic-943	319	15	from	from	ADP
hjic-943	319	16	2	2	NUM
hjic-943	319	17	to	to	ADP
hjic-943	319	18	i	i	PRON
hjic-943	319	19	during	during	ADP
hjic-943	319	20	the	the	DET
hjic-943	319	21	steady	steady	ADJ
hjic-943	319	22	state	state	NOUN
hjic-943	319	23	assumption	assumption	NOUN
hjic-943	319	24	of	of	ADP
hjic-943	319	25	internal	internal	ADJ
hjic-943	319	26	energy	energy	NOUN
hjic-943	319	27	of	of	ADP
hjic-943	319	28	liquid	liquid	NOUN
hjic-943	319	29	and	and	CCONJ
hjic-943	319	30	with	with	ADP
hjic-943	319	31	the	the	DET
hjic-943	319	32	proposed	propose	VERB
hjic-943	319	33	modification	modification	NOUN
hjic-943	319	34	of	of	ADP
hjic-943	319	35	model	model	NOUN
hjic-943	319	36	specification	specification	NOUN
hjic-943	319	37	.	.	PUNCT
hjic-943	320	1	consider	consider	VERB
hjic-943	320	2	a	a	DET
hjic-943	320	3	dynamic	dynamic	ADJ
hjic-943	320	4	process	process	NOUN
hjic-943	320	5	model	model	NOUN
hjic-943	320	6	with	with	ADP
hjic-943	320	7	differential	differential	ADJ
hjic-943	320	8	index	index	NOUN
hjic-943	320	9	2	2	NUM
hjic-943	320	10	.	.	PUNCT
hjic-943	320	11	assume	assume	VERB
hjic-943	320	12	that	that	SCONJ
hjic-943	320	13	the	the	DET
hjic-943	320	14	derivative	derivative	ADJ
hjic-943	320	15	variable	variable	NOUN
hjic-943	320	16	x	x	NOUN
hjic-943	320	17	'	'	PUNCT
hjic-943	320	18	does	do	AUX
hjic-943	320	19	not	not	PART
hjic-943	320	20	exists	exist	VERB
hjic-943	320	21	on	on	ADP
hjic-943	320	22	the	the	PRON
hjic-943	320	23	.	.	PUNCT
hjic-943	321	1	underspecified	underspecified	ADJ
hjic-943	321	2	subgraph	subgraph	NOUN
hjic-943	321	3	corresponding	correspond	VERB
hjic-943	321	4	to	to	ADP
hjic-943	321	5	the	the	DET
hjic-943	321	6	standard	standard	ADJ
hjic-943	321	7	form	form	NOUN
hjic-943	321	8	.	.	PUNCT
hjic-943	322	1	assume	assume	VERB
hjic-943	322	2	that	that	SCONJ
hjic-943	322	3	the	the	DET
hjic-943	322	4	state	state	NOUN
hjic-943	322	5	variable	variable	NOUN
hjic-943	322	6	x	x	PUNCT
hjic-943	322	7	is	be	AUX
hjic-943	322	8	in	in	ADP
hjic-943	322	9	steady	steady	ADJ
hjic-943	322	10	state	state	NOUN
hjic-943	322	11	.	.	PUNCT
hjic-943	323	1	consider	consider	VERB
hjic-943	323	2	the	the	DET
hjic-943	323	3	model	model	NOUN
hjic-943	323	4	modified	modify	VERB
hjic-943	323	5	by	by	ADP
hjic-943	323	6	the	the	DET
hjic-943	323	7	index	index	NOUN
hjic-943	323	8	reduction	reduction	NOUN
hjic-943	323	9	algorithm	algorithm	NOUN
hjic-943	323	10	and	and	CCONJ
hjic-943	323	11	its	its	PRON
hjic-943	323	12	representation	representation	NOUN
hjic-943	323	13	graph	graph	NOUN
hjic-943	323	14	for	for	ADP
hjic-943	323	15	this	this	DET
hjic-943	323	16	case	case	NOUN
hjic-943	323	17	.	.	PUNCT
hjic-943	324	1	let	let	VERB
hjic-943	324	2	the	the	DET
hjic-943	324	3	value	value	NOUN
hjic-943	324	4	of	of	ADP
hjic-943	324	5	.r	.r	NOUN
hjic-943	324	6	·	·	PUNCT
hjic-943	324	7	is	be	AUX
hjic-943	324	8	equal	equal	ADJ
hjic-943	324	9	to	to	ADP
hjic-943	324	10	zero	zero	NUM
hjic-943	324	11	hence	hence	ADV
hjic-943	324	12	the	the	DET
hjic-943	324	13	vertex	vertex	NOUN
hjic-943	324	14	.r	.r	NOUN
hjic-943	324	15	'	'	PUNCT
hjic-943	324	16	becomes	become	VERB
hjic-943	324	17	type	type	NOUN
hjic-943	324	18	<	<	X
hjic-943	324	19	g	g	PROPN
hjic-943	324	20	>	>	X
hjic-943	324	21	.	.	PUNCT
hjic-943	325	1	the	the	DET
hjic-943	325	2	effect	effect	NOUN
hjic-943	325	3	of	of	ADP
hjic-943	325	4	this	this	DET
hjic-943	325	5	modification	modification	NOUN
hjic-943	325	6	on	on	ADP
hjic-943	325	7	the	the	DET
hjic-943	325	8	structural	structural	ADJ
hjic-943	325	9	solvabilily	solvabilily	NOUN
hjic-943	325	10	is	be	AUX
hjic-943	325	11	similar	similar	ADJ
hjic-943	325	12	to	to	ADP
hjic-943	325	13	the	the	DET
hjic-943	325	14	case	case	NOUN
hjic-943	325	15	of	of	ADP
hjic-943	325	16	inde	inde	PROPN
hjic-943	325	17	:(	:(	SYM
hjic-943	325	18	l	l	NOUN
hjic-943	325	19	models	model	NOUN
hjic-943	325	20	as	as	SCONJ
hjic-943	325	21	the	the	DET
hjic-943	325	22	following	follow	VERB
hjic-943	325	23	example	example	NOUN
hjic-943	325	24	illustrates	illustrate	VERB
hjic-943	325	25	.	.	PUNCT
hjic-943	326	1	e.tample	e.tample	ADJ
hjic-943	326	2	2	2	NUM
hjic-943	326	3	tconti11ued	tconti11ue	VERB
hjic-943	326	4	}	}	PUNCT
hjic-943	326	5	.	.	PUNCT
hjic-943	327	1	consider	consider	VERB
hjic-943	327	2	again	again	ADV
hjic-943	327	3	example	example	NOUN
hjic-943	327	4	2	2	NUM
hjic-943	327	5	with	with	ADP
hjic-943	327	6	specificatioll	specificatioll	NOUN
hjic-943	327	7	2	2	NUM
hjic-943	327	8	.	.	PUNCT
hjic-943	327	9	assume	assume	VERB
hjic-943	327	10	that	that	SCONJ
hjic-943	327	11	the	the	DET
hjic-943	327	12	mass	mass	NOUN
hjic-943	327	13	of	of	ADP
hjic-943	327	14	liquid	liquid	NOUN
hjic-943	327	15	is	be	AUX
hjic-943	327	16	in	in	ADP
hjic-943	327	17	steady	steady	ADJ
hjic-943	327	18	state	state	NOUN
hjic-943	327	19	in	in	ADP
hjic-943	327	20	the	the	DET
hjic-943	327	21	tank	tank	NOUN
hjic-943	327	22	:	:	PUNCT
hjic-943	327	23	.m	.m	PUNCT
hjic-943	328	1	=	=	SYM
hjic-943	328	2	0	0	NUM
hjic-943	328	3	(	(	PUNCT
hjic-943	328	4	55	55	NUM
hjic-943	328	5	)	)	PUNCT
hjic-943	328	6	since	since	SCONJ
hjic-943	328	7	the	the	DET
hjic-943	328	8	vertex	vertex	NOUN
hjic-943	328	9	m	m	PROPN
hjic-943	328	10	'	'	PUNCT
hjic-943	328	11	does	do	AUX
hjic-943	328	12	not	not	PART
hjic-943	328	13	exist	exist	VERB
hjic-943	328	14	on	on	ADP
hjic-943	328	15	the	the	DET
hjic-943	328	16	underspecified	underspecified	ADJ
hjic-943	328	17	part	part	NOUN
hjic-943	328	18	corresponding	correspond	VERB
hjic-943	328	19	to	to	ADP
hjic-943	328	20	standard	standard	ADJ
hjic-943	328	21	fonn	fonn	NOUN
hjic-943	328	22	(	(	PUNCT
hjic-943	328	23	see	see	VERB
hjic-943	328	24	fig.5	fig.5	NOUN
hjic-943	328	25	)	)	PUNCT
hjic-943	328	26	consider	consider	VERB
hjic-943	328	27	the	the	DET
hjic-943	328	28	representation	representation	NOUN
hjic-943	328	29	graph	graph	NOUN
hjic-943	328	30	belonging	belong	VERB
hjic-943	328	31	to	to	ADP
hjic-943	328	32	the	the	DET
hjic-943	328	33	~el	~el	PROPN
hjic-943	328	34	modified	modify	VERB
hjic-943	328	35	by	by	ADP
hjic-943	328	36	the	the	DET
hjic-943	328	37	index	index	NOUN
hjic-943	328	38	reduction	reduction	NOUN
hjic-943	328	39	algorithm	algorithm	NOUN
hjic-943	328	40	(	(	PUNCT
hjic-943	328	41	see	see	VERB
hjic-943	328	42	f1g.6a	f1g.6a	NOUN
hjic-943	328	43	)	)	PUNCT
hjic-943	328	44	.	.	PUNCT
hjic-943	329	1	let	let	VERB
hjic-943	329	2	the	the	DET
hjic-943	329	3	value	value	NOUN
hjic-943	329	4	of	of	ADP
hjic-943	329	5	variable	variable	ADJ
hjic-943	329	6	m	m	PROPN
hjic-943	329	7	'	'	PUNCT
hjic-943	329	8	be	be	AUX
hjic-943	329	9	equal	equal	ADJ
hjic-943	329	10	to	to	ADP
hjic-943	329	11	zero	zero	NUM
hjic-943	329	12	.	.	PUNCT
hjic-943	330	1	hence	hence	ADV
hjic-943	330	2	the	the	DET
hjic-943	330	3	vertex	vertex	NOUN
hjic-943	330	4	m	m	PRON
hjic-943	330	5	'	'	PUNCT
hjic-943	330	6	has	have	AUX
hjic-943	330	7	label	label	VERB
hjic-943	330	8	<	<	X
hjic-943	330	9	g	g	X
hjic-943	330	10	>	>	X
hjic-943	330	11	on	on	ADP
hjic-943	330	12	all	all	DET
hjic-943	330	13	static	static	ADJ
hjic-943	330	14	graphs	graph	NOUN
hjic-943	330	15	.	.	PUNCT
hjic-943	331	1	look	look	VERB
hjic-943	331	2	for	for	ADP
hjic-943	331	3	a	a	DET
hjic-943	331	4	\'ertex	\'ertex	NOUN
hjic-943	331	5	with	with	ADP
hjic-943	331	6	label	label	NOUN
hjic-943	331	7	<	<	X
hjic-943	331	8	s	s	X
hjic-943	331	9	>	>	X
hjic-943	331	10	or	or	CCONJ
hjic-943	331	11	<	<	X
hjic-943	331	12	s	s	X
hjic-943	331	13	·	·	PUNCT
hjic-943	331	14	>	>	X
hjic-943	331	15	from	from	ADP
hjic-943	331	16	which	which	PRON
hjic-943	331	17	there	there	PRON
hjic-943	331	18	is	be	VERB
hjic-943	331	19	a	a	DET
hjic-943	331	20	directed	direct	VERB
hjic-943	331	21	path	path	NOUN
hjic-943	331	22	into	into	ADP
hjic-943	331	23	m	m	PROPN
hjic-943	331	24	·	·	PUNCT
hjic-943	331	25	.	.	PUNCT
hjic-943	332	1	this	this	DET
hjic-943	332	2	directed	direct	VERB
hjic-943	332	3	graph	graph	NOUN
hjic-943	332	4	must	must	AUX
hjic-943	332	5	be	be	AUX
hjic-943	332	6	vertex	vertex	NOUN
hjic-943	332	7	-	-	PUNCT
hjic-943	332	8	disjoint	disjoint	NOUN
hjic-943	332	9	to	to	ADP
hjic-943	332	10	the	the	DET
hjic-943	332	11	paths	path	NOUN
hjic-943	332	12	of	of	ADP
hjic-943	332	13	menger	menger	NOUN
hjic-943	332	14	-	-	PUNCT
hjic-943	332	15	type	type	NOUN
hjic-943	332	16	complete	complete	ADJ
hjic-943	332	17	linking	linking	NOUN
hjic-943	332	18	of	of	ADP
hjic-943	332	19	modified	modified	ADJ
hjic-943	332	20	model	model	NOUN
hjic-943	332	21	(	(	PUNCT
hjic-943	332	22	see	see	VERB
hjic-943	332	23	fig.6b	fig.6b	NOUN
hjic-943	332	24	)	)	PUNCT
hjic-943	332	25	.	.	PUNCT
hjic-943	333	1	there	there	PRON
hjic-943	333	2	are	be	VERB
hjic-943	333	3	two	two	NUM
hjic-943	333	4	vertices	vertex	NOUN
hjic-943	333	5	(	(	PUNCT
hjic-943	333	6	m	m	X
hjic-943	333	7	and	and	CCONJ
hjic-943	333	8	f	f	X
hjic-943	333	9	)	)	PUNCT
hjic-943	333	10	which	which	PRON
hjic-943	333	11	are	be	AUX
hjic-943	333	12	suitable	suitable	ADJ
hjic-943	333	13	under	under	ADP
hjic-943	333	14	the	the	DET
hjic-943	333	15	above	above	ADJ
hjic-943	333	16	conditions	condition	NOUN
hjic-943	333	17	.	.	PUNCT
hjic-943	334	1	choosing	choose	VERB
hjic-943	334	2	the	the	DET
hjic-943	334	3	vertex	vertex	NOUN
hjic-943	334	4	f	f	PROPN
hjic-943	334	5	and	and	CCONJ
hjic-943	334	6	dropping	drop	VERB
hjic-943	334	7	its	its	PRON
hjic-943	334	8	label	label	NOUN
hjic-943	334	9	<	<	X
hjic-943	334	10	s	s	X
hjic-943	334	11	>	>	X
hjic-943	334	12	the	the	DET
hjic-943	334	13	inlet	inlet	ADJ
hjic-943	334	14	flow	flow	NOUN
hjic-943	334	15	rate	rate	NOUN
hjic-943	334	16	of	of	ADP
hjic-943	334	17	liquid	liquid	NOUN
hjic-943	334	18	is	be	AUX
hjic-943	334	19	to	to	PART
hjic-943	334	20	be	be	AUX
hjic-943	334	21	considered	consider	VERB
hjic-943	334	22	as	as	ADP
hjic-943	334	23	an	an	DET
hjic-943	334	24	unknown	unknown	ADJ
hjic-943	334	25	variable	variable	NOUN
hjic-943	334	26	.	.	PUNCT
hjic-943	335	1	the	the	DET
hjic-943	335	2	reduced	reduce	VERB
hjic-943	335	3	graph	graph	NOUN
hjic-943	335	4	corresponding	correspond	VERB
hjic-943	335	5	to	to	ADP
hjic-943	335	6	the	the	DET
hjic-943	335	7	modified	modify	VERB
hjic-943	335	8	model	model	NOUN
hjic-943	335	9	can	can	AUX
hjic-943	335	10	be	be	AUX
hjic-943	335	11	seen	see	VERB
hjic-943	335	12	in	in	ADP
hjic-943	335	13	fig.9b	fig.9b	PROPN
hjic-943	335	14	.	.	PUNCT
hjic-943	336	1	the	the	DET
hjic-943	336	2	size	size	NOUN
hjic-943	336	3	of	of	ADP
hjic-943	336	4	linking	link	VERB
hjic-943	336	5	increases	increase	NOUN
hjic-943	336	6	from	from	ADP
hjic-943	336	7	1	1	NUM
hjic-943	336	8	to	to	ADP
hjic-943	336	9	2	2	NUM
hjic-943	336	10	.	.	PUNCT
hjic-943	337	1	the	the	DET
hjic-943	337	2	modified	modify	VERB
hjic-943	337	3	model	model	NOUN
hjic-943	337	4	is	be	AUX
hjic-943	337	5	conditionally	conditionally	ADV
hjic-943	337	6	structurally	structurally	ADV
hjic-943	337	7	solvable	solvable	ADJ
hjic-943	337	8	.	.	PUNCT
hjic-943	338	1	it	it	PRON
hjic-943	338	2	can	can	AUX
hjic-943	338	3	be	be	AUX
hjic-943	338	4	seen	see	VERB
hjic-943	338	5	that	that	SCONJ
hjic-943	338	6	the	the	DET
hjic-943	338	7	steady	steady	ADJ
hjic-943	338	8	state	state	NOUN
hjic-943	338	9	assumption	assumption	NOUN
hjic-943	338	10	for	for	ADP
hjic-943	338	11	the	the	DET
hjic-943	338	12	mass	mass	NOUN
hjic-943	338	13	of	of	ADP
hjic-943	338	14	liquid	liquid	NOUN
hjic-943	338	15	in	in	ADP
hjic-943	338	16	the	the	DET
hjic-943	338	17	tank	tank	NOUN
hjic-943	338	18	does	do	AUX
hjic-943	338	19	not	not	PART
hjic-943	338	20	change	change	VERB
hjic-943	338	21	the	the	DET
hjic-943	338	22	differential	differential	ADJ
hjic-943	338	23	index	index	NOUN
hjic-943	338	24	of	of	ADP
hjic-943	338	25	the	the	DET
hjic-943	338	26	model	model	NOUN
hjic-943	338	27	.	.	PUNCT
hjic-943	339	1	conclusion	conclusion	NOUN
hjic-943	339	2	it	it	PRON
hjic-943	339	3	is	be	AUX
hjic-943	339	4	shown	show	VERB
hjic-943	339	5	in	in	ADP
hjic-943	339	6	this	this	DET
hjic-943	339	7	paper	paper	NOUN
hjic-943	339	8	that	that	SCONJ
hjic-943	339	9	a	a	DET
hjic-943	339	10	steady	steady	ADJ
hjic-943	339	11	state	state	NOUN
hjic-943	339	12	assumption	assumption	NOUN
hjic-943	339	13	for	for	ADP
hjic-943	339	14	a	a	DET
hjic-943	339	15	state	state	NOUN
hjic-943	339	16	variable	variable	NOUN
hjic-943	339	17	x	x	PROPN
hjic-943	339	18	of	of	ADP
hjic-943	339	19	a	a	DET
hjic-943	339	20	dynamic	dynamic	ADJ
hjic-943	339	21	process	process	NOUN
hjic-943	339	22	model	model	NOUN
hjic-943	339	23	can	can	AUX
hjic-943	339	24	be	be	AUX
hjic-943	339	25	handled	handle	VERB
hjic-943	339	26	on	on	ADP
hjic-943	339	27	the	the	DET
hjic-943	339	28	representation	representation	NOUN
hjic-943	339	29	graph	graph	NOUN
hjic-943	339	30	by	by	ADP
hjic-943	339	31	modifying	modify	VERB
hjic-943	339	32	the	the	DET
hjic-943	339	33	assignment	assignment	NOUN
hjic-943	339	34	of	of	ADP
hjic-943	339	35	the	the	DET
hjic-943	339	36	derivative	derivative	ADJ
hjic-943	339	37	variable	variable	ADJ
hjic-943	339	38	vertex	vertex	NOUN
hjic-943	339	39	x	x	NOUN
hjic-943	339	40	'	'	NOUN
hjic-943	339	41	.	.	PUNCT
hjic-943	340	1	the	the	DET
hjic-943	340	2	value	value	NOUN
hjic-943	340	3	of	of	ADP
hjic-943	340	4	x	x	NOUN
hjic-943	340	5	'	'	PUNCT
hjic-943	340	6	is	be	AUX
hjic-943	340	7	equal	equal	ADJ
hjic-943	340	8	to	to	ADP
hjic-943	340	9	zero	zero	NUM
hjic-943	340	10	hence	hence	ADV
hjic-943	340	11	vertex	vertex	NOUN
hjic-943	340	12	x	x	NOUN
hjic-943	340	13	'	'	PUNCT
hjic-943	340	14	becomes	become	VERB
hjic-943	340	15	type	type	NOUN
hjic-943	340	16	<	<	X
hjic-943	340	17	g	g	NOUN
hjic-943	340	18	>	>	X
hjic-943	340	19	.	.	PUNCT
hjic-943	341	1	this	this	DET
hjic-943	341	2	modification	modification	NOUN
hjic-943	341	3	of	of	ADP
hjic-943	341	4	the	the	DET
hjic-943	341	5	original	original	ADJ
hjic-943	341	6	model	model	NOUN
hjic-943	341	7	results	result	NOUN
hjic-943	341	8	in	in	ADP
hjic-943	341	9	an	an	DET
hjic-943	341	10	overspecified	overspecified	ADJ
hjic-943	341	11	model	model	NOUN
hjic-943	341	12	therefore	therefore	ADV
hjic-943	341	13	we	we	PRON
hjic-943	341	14	must	must	AUX
hjic-943	341	15	change	change	VERB
hjic-943	341	16	the	the	DET
hjic-943	341	17	model	model	NOUN
hjic-943	341	18	specification	specification	NOUN
hjic-943	341	19	to	to	PART
hjic-943	341	20	obtain	obtain	VERB
hjic-943	341	21	structurally	structurally	ADV
hjic-943	341	22	solvable	solvable	ADJ
hjic-943	341	23	model	model	NOUN
hjic-943	341	24	.	.	PUNCT
hjic-943	342	1	after	after	ADP
hjic-943	342	2	this	this	DET
hjic-943	342	3	modification	modification	NOUN
hjic-943	342	4	of	of	ADP
hjic-943	342	5	the	the	DET
hjic-943	342	6	specification	specification	NOUN
hjic-943	342	7	the	the	DET
hjic-943	342	8	differential	differential	ADJ
hjic-943	342	9	index	index	NOUN
hjic-943	342	10	of	of	ADP
hjic-943	342	11	originally	originally	ADV
hjic-943	342	12	index	index	NOUN
hjic-943	342	13	1	1	NUM
hjic-943	342	14	model	model	NOUN
hjic-943	342	15	does	do	AUX
hjic-943	342	16	not	not	PART
hjic-943	342	17	change	change	VERB
hjic-943	342	18	.	.	PUNCT
hjic-943	343	1	in	in	ADP
hjic-943	343	2	case	case	NOUN
hjic-943	343	3	of	of	ADP
hjic-943	343	4	index	index	NOUN
hjic-943	343	5	2	2	NUM
hjic-943	343	6	models	model	NOUN
hjic-943	343	7	two	two	NUM
hjic-943	343	8	different	different	ADJ
hjic-943	343	9	cases	case	NOUN
hjic-943	343	10	are	be	AUX
hjic-943	343	11	considered	consider	VERB
hjic-943	343	12	.	.	PUNCT
hjic-943	344	1	if	if	SCONJ
hjic-943	344	2	the	the	DET
hjic-943	344	3	derivative	derivative	ADJ
hjic-943	344	4	variable	variable	ADJ
hjic-943	344	5	vertex	vertex	NOUN
hjic-943	344	6	x	x	X
hjic-943	344	7	'	'	PUNCT
hjic-943	344	8	is	be	AUX
hjic-943	344	9	on	on	ADP
hjic-943	344	10	the	the	DET
hjic-943	344	11	underspecified	underspecified	ADJ
hjic-943	344	12	subgraph	subgraph	NOUN
hjic-943	344	13	corresponding	correspond	VERB
hjic-943	344	14	to	to	ADP
hjic-943	344	15	the	the	DET
hjic-943	344	16	original	original	ADJ
hjic-943	344	17	standard	standard	ADJ
hjic-943	344	18	form	form	NOUN
hjic-943	344	19	model	model	NOUN
hjic-943	344	20	,	,	PUNCT
hjic-943	344	21	then	then	ADV
hjic-943	344	22	the	the	DET
hjic-943	344	23	standard	standard	ADJ
hjic-943	344	24	form	form	NOUN
hjic-943	344	25	of	of	ADP
hjic-943	344	26	modified	modify	VERB
hjic-943	344	27	model	model	NOUN
hjic-943	344	28	becomes	become	VERB
hjic-943	344	29	structurally	structurally	ADV
hjic-943	344	30	solvable	solvable	ADJ
hjic-943	344	31	,	,	PUNCT
hjic-943	344	32	i.e.	i.e.	X
hjic-943	344	33	the	the	DET
hjic-943	344	34	differential	differential	ADJ
hjic-943	344	35	index	index	NOUN
hjic-943	344	36	decreases	decrease	VERB
hjic-943	344	37	from	from	ADP
hjic-943	344	38	2	2	NUM
hjic-943	344	39	to	to	ADP
hjic-943	344	40	1	1	NUM
hjic-943	344	41	.	.	PUNCT
hjic-943	345	1	if	if	SCONJ
hjic-943	345	2	this	this	PRON
hjic-943	345	3	is	be	AUX
hjic-943	345	4	not	not	PART
hjic-943	345	5	the	the	DET
hjic-943	345	6	case	case	NOUN
hjic-943	345	7	,	,	PUNCT
hjic-943	345	8	then	then	ADV
hjic-943	345	9	the	the	DET
hjic-943	345	10	effect	effect	NOUN
hjic-943	345	11	of	of	ADP
hjic-943	345	12	a	a	DET
hjic-943	345	13	steady	steady	ADJ
hjic-943	345	14	state	state	NOUN
hjic-943	345	15	assumption	assumption	NOUN
hjic-943	345	16	is	be	AUX
hjic-943	345	17	the	the	DET
hjic-943	345	18	same	same	ADJ
hjic-943	345	19	as	as	ADP
hjic-943	345	20	for	for	ADP
hjic-943	345	21	the	the	DET
hjic-943	345	22	index	index	NOUN
hjic-943	345	23	1	1	NUM
hjic-943	345	24	case	case	NOUN
hjic-943	345	25	.	.	PUNCT
hjic-943	346	1	it	it	PRON
hjic-943	346	2	was	be	AUX
hjic-943	346	3	shown	show	VERB
hjic-943	346	4	that	that	SCONJ
hjic-943	346	5	the	the	DET
hjic-943	346	6	applied	apply	VERB
hjic-943	346	7	graph	graph	NOUN
hjic-943	346	8	theoretical	theoretical	ADJ
hjic-943	346	9	method	method	NOUN
hjic-943	346	10	for	for	ADP
hjic-943	346	11	structural	structural	ADJ
hjic-943	346	12	analysis	analysis	NOUN
hjic-943	346	13	of	of	ADP
hjic-943	346	14	dae	dae	NOUN
hjic-943	346	15	process	process	NOUN
hjic-943	346	16	models	model	NOUN
hjic-943	346	17	can	can	AUX
hjic-943	346	18	be	be	AUX
hjic-943	346	19	used	use	VERB
hjic-943	346	20	effectively	effectively	ADV
hjic-943	346	21	for	for	ADP
hjic-943	346	22	investigation	investigation	NOUN
hjic-943	346	23	of	of	ADP
hjic-943	346	24	the	the	DET
hjic-943	346	25	effect	effect	NOUN
hjic-943	346	26	of	of	ADP
hjic-943	346	27	modelling	model	VERB
hjic-943	346	28	assumptions	assumption	NOUN
hjic-943	346	29	.	.	PUNCT
hjic-943	347	1	further	further	ADJ
hjic-943	347	2	work	work	NOUN
hjic-943	347	3	is	be	AUX
hjic-943	347	4	directed	direct	VERB
hjic-943	347	5	towards	towards	ADP
hjic-943	347	6	analyzing	analyze	VERB
hjic-943	347	7	the	the	DET
hjic-943	347	8	effect	effect	NOUN
hjic-943	347	9	of	of	ADP
hjic-943	347	10	other	other	ADJ
hjic-943	347	11	modelling	modelling	NOUN
hjic-943	347	12	assumptions	assumption	NOUN
hjic-943	347	13	on	on	ADP
hjic-943	347	14	the	the	DET
hjic-943	347	15	structural	structural	ADJ
hjic-943	347	16	solvability	solvability	NOUN
hjic-943	347	17	properties	property	NOUN
hjic-943	347	18	in	in	ADP
hjic-943	347	19	general	general	ADJ
hjic-943	347	20	and	and	CCONJ
hjic-943	347	21	on	on	ADP
hjic-943	347	22	the	the	DET
hjic-943	347	23	differential	differential	ADJ
hjic-943	347	24	index	index	NOUN
hjic-943	347	25	,	,	PUNCT
hjic-943	347	26	in	in	ADP
hjic-943	347	27	particular	particular	ADJ
hjic-943	347	28	.	.	PUNCT
hjic-943	348	1	such	such	ADJ
hjic-943	348	2	results	result	NOUN
hjic-943	348	3	may	may	AUX
hjic-943	348	4	guide	guide	VERB
hjic-943	348	5	the	the	DET
hjic-943	348	6	modeller	modeller	NOUN
hjic-943	348	7	on	on	ADP
hjic-943	348	8	which	which	PRON
hjic-943	348	9	assumptions	assumption	NOUN
hjic-943	348	10	have	have	AUX
hjic-943	348	11	decreasing	decrease	VERB
hjic-943	348	12	effect	effect	NOUN
hjic-943	348	13	on	on	ADP
hjic-943	348	14	the	the	DET
hjic-943	348	15	differential	differential	ADJ
hjic-943	348	16	index	index	NOUN
hjic-943	348	17	and	and	CCONJ
hjic-943	348	18	warn	warn	VERB
hjic-943	348	19	him	he	PRON
hjic-943	348	20	/	/	SYM
hjic-943	348	21	her	she	PRON
hjic-943	348	22	about	about	ADP
hjic-943	348	23	assumptions	assumption	NOUN
hjic-943	348	24	which	which	PRON
hjic-943	348	25	can	can	AUX
hjic-943	348	26	increase	increase	VERB
hjic-943	348	27	the	the	DET
hjic-943	348	28	index	index	NOUN
hjic-943	348	29	.	.	PUNCT
hjic-943	349	1	acknowledgement	acknowledgement	NOUN
hjic-943	349	2	this	this	DET
hjic-943	349	3	research	research	NOUN
hjic-943	349	4	was	be	AUX
hjic-943	349	5	supported	support	VERB
hjic-943	349	6	by	by	ADP
hjic-943	349	7	the	the	DET
hjic-943	349	8	hungarian	hungarian	ADJ
hjic-943	349	9	national	national	PROPN
hjic-943	349	10	research	research	PROPN
hjic-943	349	11	fund	fund	NOUN
hjic-943	349	12	through	through	ADP
hjic-943	349	13	grant	grant	NOUN
hjic-943	349	14	no	no	PROPN
hjic-943	349	15	.	.	PUNCT
hjic-943	350	1	t	t	PROPN
hjic-943	350	2	-026575	-026575	PROPN
hjic-943	350	3	which	which	PRON
hjic-943	350	4	is	be	AUX
hjic-943	350	5	gratefully	gratefully	ADV
hjic-943	350	6	acknowledged	acknowledge	VERB
hjic-943	350	7	.	.	PUNCT
hjic-943	351	1	references	reference	NOUN
hjic-943	351	2	i.	i.	PROPN
hjic-943	351	3	brenan	brenan	PROPN
hjic-943	351	4	k.	k.	PROPN
hjic-943	351	5	e.	e.	PROPN
hjic-943	351	6	,	,	PUNCT
hjic-943	351	7	campbeu	campbeu	PROPN
hjic-943	351	8	.	.	PUNCT
hjic-943	352	1	s.	s.	PROPN
hjic-943	352	2	l.	l.	PROPN
hjic-943	352	3	and	and	CCONJ
hjic-943	352	4	pe'fzoi.d	pe'fzoi.d	PROPN
hjic-943	352	5	l.	l.	PROPN
hjic-943	352	6	r.	r.	PROPN
hjic-943	352	7	:	:	PUNCT
hjic-943	352	8	numerical	numerical	ADJ
hjic-943	352	9	solution	solution	NOUN
hjic-943	352	10	of	of	ADP
hjic-943	352	11	initial	initial	ADJ
hjic-943	352	12	value	value	NOUN
hjic-943	352	13	problems	problem	NOUN
hjic-943	352	14	in	in	ADP
hjic-943	352	15	differentialalgebraic	differentialalgebraic	PROPN
hjic-943	352	16	equations	equation	NOUN
hjic-943	352	17	north	north	NOUN
hjic-943	352	18	-	-	PUNCT
hjic-943	352	19	holland	holland	PROPN
hjic-943	352	20	,	,	PUNCT
hjic-943	352	21	new	new	PROPN
hjic-943	352	22	york	york	PROPN
hjic-943	352	23	,	,	PUNCT
hjic-943	352	24	1989	1989	NUM
hjic-943	352	25	2	2	NUM
hjic-943	352	26	.	.	PUNCT
hjic-943	352	27	duff	duff	PROPN
hjic-943	352	28	1	1	NUM
hjic-943	352	29	.	.	PUNCT
hjic-943	352	30	:	:	PUNCT
hjic-943	353	1	analysis	analysis	NOUN
hjic-943	353	2	of	of	ADP
hjic-943	353	3	sparse	sparse	ADJ
hjic-943	353	4	systems	system	NOUN
hjic-943	353	5	,	,	PUNCT
hjic-943	353	6	d.phil	d.phil	ADJ
hjic-943	353	7	oxford	oxford	PROPN
hjic-943	353	8	university	university	NOUN
hjic-943	353	9	,	,	PUNCT
hjic-943	353	10	1972	1972	NUM
hjic-943	353	11	3	3	NUM
hjic-943	353	12	.	.	PUNCT
hjic-943	353	13	hairer	hairer	PROPN
hjic-943	353	14	e.	e.	PROPN
hjic-943	353	15	,	,	PUNCT
hjic-943	353	16	lubich	lubich	PROPN
hjic-943	353	17	c.	c.	PROPN
hjic-943	353	18	and	and	CCONJ
hjic-943	353	19	roche	roche	PROPN
hjic-943	353	20	m.	m.	NOUN
hjic-943	353	21	:	:	PUNCT
hjic-943	353	22	the	the	DET
hjic-943	353	23	numerical	numerical	ADJ
hjic-943	353	24	solution	solution	NOUN
hjic-943	353	25	of	of	ADP
hjic-943	353	26	differential	differential	ADJ
hjic-943	353	27	-	-	PUNCT
hjic-943	353	28	algebraic	algebraic	ADJ
hjic-943	353	29	systems	system	NOUN
hjic-943	353	30	by	by	ADP
hjic-943	353	31	runge	runge	NOUN
hjic-943	353	32	-	-	PUNCT
hjic-943	353	33	kutta	kutta	NOUN
hjic-943	353	34	methods	method	NOUN
hjic-943	353	35	,	,	PUNCT
hjic-943	353	36	springer­	springer­	PROPN
hjic-943	353	37	verlag	verlag	PROPN
hjic-943	353	38	,	,	PUNCT
hjic-943	353	39	berlin	berlin	PROPN
hjic-943	353	40	,	,	PUNCT
hjic-943	353	41	heidelberg	heidelberg	PROPN
hjic-943	353	42	,	,	PUNCT
hjic-943	353	43	1989	1989	NUM
hjic-943	353	44	4	4	NUM
hjic-943	353	45	.	.	PUNCT
hjic-943	354	1	hangos	hangos	PROPN
hjic-943	354	2	k.	k.	PROPN
hjic-943	354	3	m.	m.	PROPN
hjic-943	354	4	and	and	CCONJ
hjic-943	354	5	cameron	cameron	PROPN
hjic-943	354	6	i.	i.	PROPN
hjic-943	354	7	t.	t.	PROPN
hjic-943	354	8	:	:	PUNCT
hjic-943	354	9	process	process	NOUN
hjic-943	354	10	modelling	modelling	NOUN
hjic-943	354	11	and	and	CCONJ
hjic-943	354	12	model	model	NOUN
hjic-943	354	13	analysis	analysis	NOUN
hjic-943	354	14	,	,	PUNCT
hjic-943	354	15	academic	academic	ADJ
hjic-943	354	16	press	press	NOUN
hjic-943	354	17	,	,	PUNCT
hjic-943	354	18	new	new	PROPN
hjic-943	354	19	york	york	PROPN
hjic-943	354	20	,	,	PUNCT
hjic-943	354	21	london	london	PROPN
hjic-943	354	22	,	,	PUNCT
hjic-943	354	23	2001	2001	NUM
hjic-943	354	24	5	5	NUM
hjic-943	354	25	.	.	PUNCT
hjic-943	354	26	iri	iri	PROPN
hjic-943	354	27	m.	m.	NOUN
hjic-943	354	28	,	,	PUNCT
hjic-943	354	29	tsunekawa	tsunekawa	PROPN
hjic-943	354	30	j.	j.	PROPN
hjic-943	354	31	and	and	CCONJ
hjic-943	354	32	yaj.ima	yaj.ima	PROPN
hjic-943	354	33	k.	k.	NOUN
hjic-943	354	34	:	:	PUNCT
hjic-943	354	35	information	information	NOUN
hjic-943	354	36	processing	processing	NOUN
hjic-943	354	37	,	,	PUNCT
hjic-943	354	38	1972	1972	NUM
hjic-943	354	39	,	,	PUNCT
hjic-943	354	40	71	71	NUM
hjic-943	354	41	,	,	PUNCT
hjic-943	354	42	1150	1150	NUM
hjic-943	354	43	-	-	SYM
hjic-943	354	44	1155	1155	NUM
hjic-943	354	45	(	(	PUNCT
hjic-943	354	46	proc	proc	NOUN
hjic-943	354	47	.	.	PUNCT
hjic-943	355	1	ifip	ifip	PROPN
hjic-943	355	2	congr	congr	NOUN
hjic-943	355	3	.	.	PUNCT
hjic-943	356	1	71	71	NUM
hjic-943	356	2	,	,	PUNCT
hjic-943	356	3	vol	vol	NOUN
hjic-943	356	4	.	.	NOUN
hjic-943	357	1	2	2	NUM
hjic-943	357	2	.	.	NUM
hjic-943	357	3	,	,	PUNCT
hjic-943	357	4	(	(	PUNCT
hjic-943	357	5	appl	appl	PROPN
hjic-943	357	6	.	.	PUNCT
hjic-943	357	7	)	)	PUNCT
hjic-943	357	8	)	)	PUNCT
hjic-943	358	1	6	6	X
hjic-943	358	2	.	.	PUNCT
hjic-943	358	3	leitold	leitold	ADJ
hjic-943	358	4	a.	a.	NOUN
hjic-943	358	5	and	and	CCONJ
hjic-943	358	6	hangos	hangos	PROPN
hjic-943	358	7	k.	k.	PROPN
hjic-943	358	8	m.	m.	PROPN
hjic-943	358	9	:	:	PUNCT
hjic-943	358	10	on	on	ADP
hjic-943	358	11	algebraic	algebraic	ADJ
hjic-943	358	12	model	model	NOUN
hjic-943	358	13	transformations	transformation	NOUN
hjic-943	358	14	.	.	PUNCT
hjic-943	359	1	proc	proc	NOUN
hjic-943	359	2	.	.	PUNCT
hjic-943	360	1	of	of	ADP
hjic-943	360	2	cmp'98	cmp'98	ADJ
hjic-943	360	3	prague	prague	NOUN
hjic-943	360	4	,	,	PUNCT
hjic-943	360	5	czech	czech	PROPN
hjic-943	360	6	rep	rep	PROPN
hjic-943	360	7	.	.	PROPN
hjic-943	360	8	pp	pp	PROPN
hjic-943	360	9	.	.	PUNCT
hjic-943	361	1	133	133	NUM
hjic-943	361	2	-	-	SYM
hjic-943	361	3	138	138	NUM
hjic-943	361	4	,	,	PUNCT
hjic-943	361	5	1998	1998	NUM
hjic-943	361	6	71	71	NUM
hjic-943	361	7	7	7	NUM
hjic-943	361	8	.	.	PUNCT
hjic-943	362	1	leitold	leitold	ADJ
hjic-943	362	2	,	,	PUNCT
hjic-943	362	3	a.	a.	PROPN
hjic-943	362	4	and	and	CCONJ
hjic-943	362	5	hangos	hangos	PROPN
hjic-943	362	6	k.	k.	PROPN
hjic-943	362	7	m.	m.	PROPN
hjic-943	362	8	:	:	PUNCT
hjic-943	362	9	computers	computer	NOUN
hjic-943	362	10	and	and	CCONJ
hjic-943	362	11	chemical	chemical	NOUN
hjic-943	362	12	engineering	engineering	NOUN
hjic-943	362	13	,	,	PUNCT
hjic-943	362	14	2001	2001	NUM
hjic-943	362	15	,	,	PUNCT
hjic-943	362	16	in	in	ADP
hjic-943	362	17	press	press	NOUN
hjic-943	362	18	.	.	PUNCT
hjic-943	363	1	8	8	NUM
hjic-943	363	2	.	.	X
hjic-943	363	3	moe	moe	PROPN
hjic-943	363	4	h.	h.	PROPN
hjic-943	363	5	i.	i.	PROPN
hjic-943	363	6	:	:	PUNCT
hjic-943	363	7	dynamic	dynamic	ADJ
hjic-943	363	8	process	process	NOUN
hjic-943	363	9	simulation	simulation	NOUN
hjic-943	363	10	,	,	PUNCT
hjic-943	363	11	studies	study	NOUN
hjic-943	363	12	on	on	ADP
hjic-943	363	13	modeling	modeling	NOUN
hjic-943	363	14	and	and	CCONJ
hjic-943	363	15	index	index	NOUN
hjic-943	363	16	reduction	reduction	NOUN
hjic-943	363	17	,	,	PUNCT
hjic-943	363	18	phd	phd	NOUN
hjic-943	363	19	thesis	thesis	NOUN
hjic-943	363	20	,	,	PUNCT
hjic-943	363	21	university	university	NOUN
hjic-943	363	22	of	of	ADP
hjic-943	363	23	trondheim	trondheim	PROPN
hjic-943	363	24	,	,	PUNCT
hjic-943	363	25	1995	1995	NUM
hjic-943	363	26	9	9	NUM
hjic-943	363	27	.	.	PUNCT
hjic-943	363	28	murota	murota	NOUN
hjic-943	363	29	,	,	PUNCT
hjic-943	363	30	k.	k.	NOUN
hjic-943	363	31	:	:	PUNCT
hjic-943	364	1	systems	system	NOUN
hjic-943	364	2	analysis	analysis	NOUN
hjic-943	364	3	by	by	ADP
hjic-943	364	4	graphs	graph	NOUN
hjic-943	364	5	and	and	CCONJ
hjic-943	364	6	matroids	matroid	NOUN
hjic-943	364	7	,	,	PUNCT
hjic-943	364	8	springer	springer	NOUN
hjic-943	364	9	-	-	PUNCT
hjic-943	364	10	verlag	verlag	PROPN
hjic-943	364	11	berlin	berlin	PROPN
hjic-943	364	12	,	,	PUNCT
hjic-943	364	13	1987	1987	NUM
hjic-943	364	14	10	10	NUM
hjic-943	364	15	.	.	PUNCT
hjic-943	365	1	sargent	sargent	PROPN
hjic-943	365	2	,	,	PUNCT
hjic-943	365	3	r.	r.	PROPN
hjic-943	365	4	w.	w.	PROPN
hjic-943	365	5	h.	h.	PROPN
hjic-943	365	6	and	and	CCONJ
hjic-943	365	7	westerberg	westerberg	PROPN
hjic-943	365	8	a.	a.	PROPN
hjic-943	365	9	w.	w.	PROPN
hjic-943	365	10	:	:	PUNCT
hjic-943	365	11	trans	trans	PROPN
hjic-943	365	12	.	.	PROPN
hjic-943	365	13	inst	inst	PROPN
hjic-943	365	14	.	.	PUNCT
hjic-943	366	1	chern	chern	PROPN
hjic-943	366	2	.	.	PUNCT
hjic-943	367	1	eng	eng	PROPN
hjic-943	367	2	.	.	PROPN
hjic-943	367	3	,	,	PUNCT
hjic-943	367	4	1964,42	1964,42	PROPN
hjic-943	367	5	,	,	PUNCT
hjic-943	367	6	190	190	NUM
hjic-943	367	7	-	-	SYM
hjic-943	367	8	197	197	NUM
hjic-943	367	9	11	11	NUM
hjic-943	367	10	.	.	PUNCT
hjic-943	368	1	unger	unger	PROPN
hjic-943	368	2	j.	j.	PROPN
hjic-943	368	3	,	,	PUNCT
hjic-943	368	4	kroner	kroner	PROPN
hjic-943	368	5	a.	a.	PROPN
hjic-943	368	6	and	and	CCONJ
hjic-943	368	7	marquardt	marquardt	PROPN
hjic-943	368	8	w.	w.	PROPN
hjic-943	368	9	:	:	PUNCT
hjic-943	368	10	computers	computer	NOUN
hjic-943	368	11	chem	chem	NOUN
hjic-943	368	12	.	.	PUNCT
hjic-943	369	1	engng	engng	ADJ
hjic-943	369	2	,	,	PUNCT
hjic-943	369	3	1995	1995	NUM
hjic-943	369	4	,	,	PUNCT
hjic-943	369	5	19	19	NUM
hjic-943	369	6	,	,	PUNCT
hjic-943	369	7	8	8	NUM
hjic-943	369	8	,	,	PUNCT
hjic-943	369	9	867·882	867·882	PROPN
hjic-943	369	10	12	12	NUM
hjic-943	369	11	.	.	PUNCT
hjic-943	370	1	yajima	yajima	PROPN
hjic-943	370	2	k.	k.	PROPN
hjic-943	370	3	and	and	CCONJ
hjic-943	370	4	tsunekawa	tsunekawa	PROPN
hjic-943	370	5	j.	j.	PROPN
hjic-943	370	6	:	:	PUNCT
hjic-943	370	7	graphical	graphical	ADJ
hjic-943	370	8	techniques	technique	NOUN
hjic-943	370	9	used	use	VERB
hjic-943	370	10	for	for	ADP
hjic-943	370	11	a	a	DET
hjic-943	370	12	dynamic	dynamic	ADJ
hjic-943	370	13	chemical	chemical	NOUN
hjic-943	370	14	process	process	NOUN
hjic-943	370	15	simulation	simulation	NOUN
hjic-943	370	16	,	,	PUNCT
hjic-943	370	17	proc	proc	PROPN
hjic-943	370	18	.	.	PUNCT
hjic-943	371	1	loth	loth	PROPN
hjic-943	371	2	ifip	ifip	PROPN
hjic-943	371	3	conf	conf	NOUN
hjic-943	371	4	.	.	PUNCT
hjic-943	372	1	new	new	PROPN
hjic-943	372	2	york	york	PROPN
hjic-943	372	3	city	city	PROPN
hjic-943	372	4	,	,	PUNCT
hjic-943	372	5	1981	1981	NUM
hjic-943	372	6	(	(	PUNCT
hjic-943	372	7	in	in	ADP
hjic-943	372	8	eds	ed	NOUN
hjic-943	372	9	.	.	PUNCT
hjic-943	373	1	r.f	r.f	PROPN
hjic-943	373	2	.	.	PROPN
hjic-943	373	3	denrick	denrick	PROPN
hjic-943	373	4	and	and	CCONJ
hjic-943	373	5	f.	f.	PROPN
hjic-943	373	6	kozin	kozin	PROPN
hjic-943	373	7	,	,	PUNCT
hjic-943	373	8	lecture	lecture	NOUN
hjic-943	373	9	notes	note	NOUN
hjic-943	373	10	in	in	ADP
hjic-943	373	11	control	control	NOUN
hjic-943	373	12	and	and	CCONJ
hjic-943	373	13	information	information	NOUN
hjic-943	373	14	sciences	science	NOUN
hjic-943	373	15	,	,	PUNCT
hjic-943	373	16	38	38	NUM
hjic-943	373	17	,	,	PUNCT
hjic-943	373	18	springer	springer	NOUN
hjic-943	373	19	,	,	PUNCT
hjic-943	373	20	berlin	berlin	PROPN
hjic-943	373	21	,	,	PUNCT
hjic-943	373	22	826	826	NUM
hjic-943	373	23	-	-	SYM
hjic-943	373	24	833	833	NUM
hjic-943	373	25	,	,	PUNCT
hjic-943	373	26	1982	1982	NUM
hjic-943	373	27	)	)	PUNCT
hjic-943	373	28	page	page	NOUN
hjic-943	373	29	58	58	NUM
hjic-943	373	30	page	page	NOUN
hjic-943	373	31	59	59	NUM
hjic-943	373	32	page	page	NOUN
hjic-943	373	33	60	60	NUM
hjic-943	373	34	page	page	NOUN
hjic-943	373	35	61	61	NUM
hjic-943	373	36	page	page	NOUN
hjic-943	373	37	62	62	NUM
hjic-943	373	38	page	page	NOUN
hjic-943	373	39	63	63	NUM
hjic-943	373	40	page	page	NOUN
hjic-943	373	41	64	64	NUM
hjic-943	373	42	page	page	NOUN
hjic-943	373	43	65	65	NUM
hjic-943	373	44	page	page	NOUN
hjic-943	373	45	66	66	NUM
hjic-943	373	46	page	page	NOUN
hjic-943	373	47	67	67	NUM
hjic-943	373	48	page	page	NOUN
hjic-943	373	49	68	68	NUM